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 Reutenauer, Christophe, author.
 First edition.  Oxford : Oxford University Press, 2019.
 Description
 Book — 1 online resource.
 Summary

In 1875, Elwin Bruno Christoffel introduced a special class of words on a binary alphabet linked to continued fractions which would go onto be known as Christoffel words. Some years later, Andrey Markoff published his famous theory, the now called Markoff theory. It characterized certain quadratic forms and certain real numbers by extremal inequalities. Both classes are constructed using certain natural numbers  known as Markoff numbers  and they are characterized by a certain Diophantine equality. More basically, they are constructed using certain words  essentially the Christoffel words. The link between Christoffel words and the theory of Markoff was noted by Ferdinand Frobenius in 1913, but has been neglected in recent times. Motivated by this overlooked connection, this book looks to expand on the relationship between these two areas. Part 1 focuses on the classical theory of Markoff, while Part II explores the more advanced and recent results of the theory of Christoffel words.
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2. Approximate quantum Markov chains [2018]
 Sutter, David, author.
 Cham, Switzerland : Springer, [2018]
 Description
 Book — 1 online resource. Digital: text file; PDF.
 Summary

 Introduction. Classical Markov chains. Quantum Markov chains. Outline. Preliminaries. Notation. Schatten norms. Functions on Hermitian operators. Quantum channels. Entropy measures. Background and further reading. Tools for noncommuting operators. Pinching. Complex interpolation theory. Background and further reading. Multivariate trace inequalities. Motivation. Multivariate ArakiLiebThirring inequality. Multivariate GoldenThompson inequality. Multivariate logarithmic trace inequality. Background and further reading. Approximate quantum Markov chains. Quantum Markov chains. Sufficient criterion for approximate recoverability. Necessary criterion for approximate recoverability. Strengthened entropy inequalities. Background and further reading. A A large conditional mutual information does not imply bad recovery. B Example showing the optimality of the Lmaxterm. C Solutions to exercises. References. Index.
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 Çetin, Umut, author.
 New York, NY, U.S.A. : Springer, [2018]
 Description
 Book — 1 online resource.
 Summary

 Markov processes. Stochastic Differential Equations and Martingale Problems. Stochastic Filtering. Static Markov Bridges and Enlargement of Filtrations. Dynamic Bridges. Financial markets with informational asymmetries and equilibrium. KyleBack model with dynamic information: no default case. Appendix A.
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 Van der Hoek, John, author.
 Cambridge, United Kingdom ; New York : Cambridge University Press, 2018.
 Description
 Book — x, 174 pages ; 23 cm.
 Summary

 Preface
 1. Observed Markov chains
 2. Estimation of an observed Markov chain
 3. Hidden Markov models
 4. Filters and smoothers
 5. The Viterbi algorithm
 6. The EM algorithm
 7. A new Markov chain model
 8. SemiMarkov models
 9. Hidden semiMarkov models
 10. Filters for hidden semiMarkov models Appendix A. Higher order chains Appendix B. An example of a second order chain Appendix C. A conditional Bayes theorem Appendix D. On conditional expectations Appendix E. Some molecular biology Appendix F. Earlier applications of hidden Markov chain models References Index.
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QA274.7 .V356 2018  Unavailable In process Request 
 Van der Hoek, John, author.
 Cambridge, United Kingdom ; New York : Cambridge University Press, 2018.
 Description
 Book — 1 online resource.
 Summary

 Preface
 1. Observed Markov chains
 2. Estimation of an observed Markov chain
 3. Hidden Markov models
 4. Filters and smoothers
 5. The Viterbi algorithm
 6. The EM algorithm
 7. A new Markov chain model
 8. SemiMarkov models
 9. Hidden semiMarkov models
 10. Filters for hidden semiMarkov models Appendix A. Higher order chains Appendix B. An example of a second order chain Appendix C. A conditional Bayes theorem Appendix D. On conditional expectations Appendix E. Some molecular biology Appendix F. Earlier applications of hidden Markov chain models References Index.
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 Lupu, Titus, author.
 Paris : Société mathématique de France, 2018.
 Description
 Book — 158 pages ; 24 cm.
 Online
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Shelved by Series title N.S. NO.158  Unknown 
 Kochs, HansDieter, author.
 Cham, Switzerland : Springer, [2018]
 Description
 Book — 1 online resource. Digital: text file; PDF.
 Summary

 Definitions and objective. Brief review of system dependability approaches. Network approaches. Statespace approach. Markov minimal cut (MMC) approach. Uncertainty.
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 Théorie asymptotique des processus aléatoires faiblement dépendants. English
 Rio, Emmanuel, author.
 Berlin, Germany : Springer Nature, [2017]
 Description
 Book — xviii, 204 pages ; 24 cm.
 Summary

 Introduction. Variance of partial sums. Algebraic moments. Elementary exponential inequalities. Maximal inequalities and strong laws. Central limit theorems. Coupling and mixing. FukNagaev inequalities, applications. Empirical distribution functions. Empirical processes indexed by classes of functions. Irreducible Markov chains. Appendices. References. Index.
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QA295 .R5613 2017  Unknown 
 Blasco, Agustín, author.
 Cham : Springer, [2017]
 Description
 Book — xviii, 275 pages : illustrations (some color) ; 24 cm
 Summary

 Foreword Notation
 1. Do we understand classical statistics? 1.1. Historical introduction 1.2. Test of hypothesis 1.2.1. The procedure 1.2.2. Common misinterpretations 1.3. Standard errors and Confidence intervals 1.3.1. Definition of standard error and confidence interval 1.3.2. Common misinterpretations 1.4. Bias and Risk of an estimator 1.4.1. Unbiased estimators 1.4.2. Common misinterpretations 1.5. Fixed and random effects
 1.5.1. Definition of "fixed" and "random" effects
 1.5.2. Shrinkage of random effects estimates
 1.5.3. Bias, variance and Risk of an estimator when the effect is fixed or random
 1.5.4. Common misinterpretations 1.6. Likelihood 1.6.1. Definition of likelihood 1.6.2. The method of maximum likelihood 1.6.3. Common misinterpretations Appendix 1.1 Appendix 1.2 Appendix 1.3 Appendix 1.4
 2. The Bayesian choice 2.1. Bayesian inference
 2.1.1. The foundations of Bayesian inference
 2.1.2. Bayes theorem
 2.1.3. Prior information 2.2. Features of Bayesian inference 2.2.1. Point estimates: Mean, median, mode 2.2.2. Credibility intervals 2.2.3. Marginalisation 2.3. Test of hypotheses 2.3.1. Model choice 2.3.2. Bayes factors 2.3.3. Model averaging 2.4. Common misinterpretations 2.5. Bayesian Inference in practice 2.6. Advantages of Bayesian inference Appendix 2.1 Appendix 2.2 Appendix 2.3
 3. Posterior distributions 3.1. Notation 3.2. Probability density function
 3.2.1. Definition
 3.2.2. Transformed densities 3.3. Features of a distribution 3.3.1. Mean 3.3.2. Median 3.3.3. Mode 3.3.4. Credibility intervals 3.4. Conditional distribution
 3.4.1. Bayes Theorem
 3.4.2. Conditional distribution of the sample of a Normal distribution
 3.4.3. Conditional distribution of the variance of a Normal distribution
 3.4.4. Conditional distribution of the mean of a Normal distribution 3.5. Marginal distribution
 3.5.1. Definition
 3.5.2. Marginal distribution of the variance of a normal distribution
 3.5.3. Marginal distribution of the mean of a normal distribution Appendix 3.1 Appendix 3.2 Appendix 3.3 Appendix 3.4
 4. MCMC 4.1. Samples of Marginal Posterior distributions
 4.1.1. Taking samples of Marginal Posterior distributions 4.1.2. Making inferences from samples of Marginal Posterior distributions 4.2. Gibbs sampling 4.2.1. How it works 4.2.2. Why it works 4.2.3. When it works 4.2.4. Gibbs sampling features 4.2.5. Example 4.3. Other MCMC methods 4.3.1. AcceptanceRejection 4.3.2. Metropolis Appendix 4.1
 5. The "baby" model 5.1. The model 5.2. Analytical solutions 5.2.1. Marginal posterior distribution of the mean and variance 5.2.2. Joint posterior distribution of the mean and variance 5.2.3. Inferences 5.3. Working with MCMC
 5.3.1. The process 5.3.2. Using Flat priors 5.3.3. Using vague informative priors 5.3.4. Common misinterpretations Appendix 5.1 Appendix 5.2 Appendix 5.3
 6. The linear model. I. The "fixed" effects model
 6.1. The model
 6.1.1. The model
 6.1.2. Example
 6.1.3. Common misinterpretations
 6.2. Marginal posterior distributions via MCMC using Flat priors
 6.2.1. Joint posterior distribution
 6.2.2. Conditional distributions
 6.2.3. Gibbs sampling 6.3. Marginal posterior distributions via MCMC using vague informative priors
 6.3.1. Vague in formative priors
 6.3.2. Conditional distributions. 6.4. Least Squares as a Bayesian Estimator Appendix 6.1 Appendix 6.2
 7. The linear model. II. The "mixed" model 7.1. The mixed model with repeated records
 7.1.1. The model 7.1.2. Common misinterpretations 7.1.3. Marginal posterior distributions via MCMC 7.1.4. Gibbs sampling 7.2. The genetic animal model
 7.2.1. The model <
 7.2.2. Marginal posterior distributions via MCMC 7.3. Bayesian interpretation of BLUP and REML
 7.3.1. BLUP in a frequentist context
 7.3.2. BLUP as a Bayesian estimator
 7.3.3. REML as a Bayesian estimator 7.4. The multitrait model 7.4.1. The model 7.4.2. Data augmentation 7.4.3. More complex models Appendix 7.1
 8. A scope of the possibilities of Bayesian inference + MCMC 8.1. Nested models: Examples in growth curves
 8.1.1. The model
 8.1.2. Marginal posterior distributions
 8.1.3. More complex models 8.2. Modelling residuals. Examples in canalization.
 8.2.1. The model
 8.2.2. Marginal posterior distributions
 8.2.3. More complex models 8.3. Modelling priors: Examples in genomic selection
 8.3.1. The model 8.3.2. RRBLUP
 8.3.3. Bayes A
 8.3.4. Bayes B
 8.3.5. Bayes C and Bayes Cp
 8.3.6. Bayes L (Bayesian Lasso)
 8.3.7. Bayesian alphabet in practice Appendix 8.1
 9. Prior information Abstract 9.1. Exact prior information 9.1.1. Prior information 9.1.2. Posterior probabilities with exact prior information 9.1.3. Influence of prior information in posterior probabilities 9.2. Vague prior information
 9.2.1. A vague definition of vague prior information 9.2.2. Examples of the use of vague prior information 9.3. No prior information 9.3.1. Flat priors 9.3.2. Jeffrey's priors 9.3.3. Bernardo's "Reference" priors 9.4. Improper priors 9.5. The Achilles heel of Bayesian inference Appendix 9.1 Appendix 9.2
 10. Model choice 10.1 Model selection 10.1.1. The purpose of model selection 10.1.2. Fitting data vs predicting new records 10.1.3. Common misinterpretations 10.2. Hypothesis tests
 10.2.1. Likelihood ratio test and other frequentist tests
 10.2.2. Bayesian model choice 10.3. The concept of Information
 10.3.1. Fisher information 10.3.2. Shannon information and entropy 10.3.3. Kullback Information and Divergence 10.4. Model selection criteria 10.4.1. Akaike Information Criterion (AIC) 10.4.2. Deviance Information Criterion (DIC) 10.4.3. Bayesian Information Criterion (BIC) 10.4.4. Model choice in practice Appendix 10.1 Appendix 10.2 Appendix 10.3 Appendix 10.4 Appendix: Three new dialogues between Hylas and Filonus on scientific inference References â .
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QA279.5 .B583 2017  Unknown 
10. Markov chains and mixing times [2017]
 Levin, David Asher, 1971 author.
 Second edition.  Providence, Rhode Island : American Mathematical Society, 2017.
 Description
 Book — 1 online resource (448 pages) : illustrations
 Summary

 Basic methods and examples: Introduction to finite Markov chainsClassical (and useful) Markov chainsMarkov chain Monte Carlo: Metropolis and Glauber chainsIntroduction to Markov chain mixingCouplingStrong stationary timesLower bounds on mixing timesThe symmetric group and shuffling cardsRandom walks on networksHitting timesCover timesEigenvaluesThe plot thickens: Eigenfunctions and comparison of chainsThe transportation metric and path couplingThe Ising modelFrom shuffling cards to shuffling genesMartingales and evolving setsThe cutoff phenomenonLamplighter walksContinuoustime chainsCountable state space chainsMonotone chainsThe exclusion processCesaro mixing time, stationary times, and hitting large setsCoupling from the pastOpen problemsBackground materialIntroduction to simulationErgodic theoremSolutions to selected exercisesBibliographyNotation indexIndex.
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11. Markov chains and mixing times [2017]
 Levin, David Asher, 1971 author.
 Second edition.  Providence, Rhode Island : American Mathematical Society, [2017]
 Description
 Book — 1 online resource (xvi, 447 pages) : illustrations.
 Summary

 Basic methods and examples: Introduction to finite Markov chainsClassical (and useful) Markov chainsMarkov chain Monte Carlo: Metropolis and Glauber chainsIntroduction to Markov chain mixingCouplingStrong stationary timesLower bounds on mixing timesThe symmetric group and shuffling cardsRandom walks on networksHitting timesCover timesEigenvaluesThe plot thickens: Eigenfunctions and comparison of chainsThe transportation metric and path couplingThe Ising modelFrom shuffling cards to shuffling genesMartingales and evolving setsThe cutoff phenomenonLamplighter walksContinuoustime chainsCountable state space chainsMonotone chainsThe exclusion processCesaro mixing time, stationary times, and hitting large setsCoupling from the pastOpen problemsBackground materialIntroduction to simulationErgodic theoremSolutions to selected exercisesBibliographyNotation indexIndex.
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 Gagniuc, Paul A., author.
 Hoboken, NJ : John Wiley & Sons, [2017]
 Description
 Book — 1 online resource. Digital: data file.
 Summary

 Abstract ix Preface xi Acknowledgments xiii About the CompanionWebsite xv
 1 Historical Notes
 1 1.1 Introduction
 1 1.2 On theWings of Dependent Variables
 2 1.3 From Bernoulli to Markov
 5
 2 FromObservation to Simulation
 9 2.1 Introduction
 9 2.2 Stochastic Matrices
 9 2.3 Transition Probabilities
 11 2.4 The Simulation of a TwoState Markov Chain
 14
 3 Building the Stochastic Matrix
 25 3.1 Introduction
 25 3.2 Building a Stochastic Matrix from Events
 25 3.3 Building a Stochastic Matrix from Percentages
 32
 4 Predictions Using TwoState Markov Chains
 37 4.1 Introduction
 37 4.2 Performing the Predictions by Using the Stochastic Matrix
 37 4.3 The Steady State of a Markov Chain
 46 4.4 The LongRun Distribution of a Markov Chain
 55
 5 Predictions Using nState Markov Chains
 61 5.1 Introduction
 61 5.2 Predictions by Using the ThreeState Markov Chain
 61 5.3 Predictions by Using the FourState Markov Chain
 71 5.4 Predictions by Using nState Markov Chains
 80 5.5 Markov Chain Modeling on Measurements
 84
 6 AbsorbingMarkov Chains
 93 6.1 Introduction
 93 6.2 The Absorbing State
 93
 7 The Average Time Spent in Each State
 99 7.1 Introduction
 99 7.2 The Proportion of Balls in the System
 99 7.3 The Average Time Spent in A Particular State
 100 7.4 Exemplification of the Average Time and Proportions
 101
 8 Discussions on Different Configurations of Chains
 107 8.1 Introduction
 107 8.2 Examples of TwoState Diagrams
 113 8.3 Examples of ThreeState Diagrams
 115 8.4 Examples of FourState Diagrams
 117 8.5 Examples of State Diagrams Divided into Classes
 123 8.6 Examples of State Diagrams with Absorbing States
 127 8.7 The Gambler s Ruin
 128
 9 The Simulation of an nState Markov Chain
 131 9.1 Introduction
 131 9.2 The Simulation of Behavior
 131 9.3 Simulation of Different Chain Configurations
 145 A Supporting Algorithms in PHP
 165 B Supporting Algorithms in Javascript
 193 C Syntax Equivalence between Languages
 223 Glossary
 225 References
 227 Index 231.
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 Bladt, Mogens, author.
 New York, NY : Springer, [2017]
 Description
 Book — xvii, 736 pages ; 25 cm.
 Summary

 Preface. Notation. Preliminaries on Stochastic Processes. Martingales and More General Markov Processes. Phasetype Distributions. Matrixexponential Distributions. Renewal Theory. Random Walks. Regeneration and Harris Chains. Multivariate Distributions. Markov Additive Processes. Markovian Point Processes. Some Applications to Risk Theory. Statistical Methods for Markov Processes. Estimation of Phasetype Distributions. Bibliographic Notes. Appendix.
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QA274.7 .B53 2017  Unknown 
14. Nonlinearly perturbed semiMarkov processes [2017]
 Silʹvestrov, D. S. (Dmitriĭ Sergeevich)
 Cham : Springer, [2017]
 Description
 Book — 1 online resource.
 Summary

 Laurent Asymptotic Expansions. Asymptotic Expansions for Moments of Hitting Times for Nonlinearly Perturbed SemiMarkov Processes. Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed SemiMarkov Processes. Nonlinearly Perturbed BirthDeathType SemiMarkov Processes. Examples and Survey of Applied Perturbed Stochastic Models. A. Methodological and Bibliographical Remarks.
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 Rudnicki, Ryszard, author.
 Cham, Switzerland : Springer, [2017]
 Description
 Book — 1 online resource.
 Summary

 Preface; Acknowledgements; Contents;
 1 Biological Models; 1.1 Introduction; 1.2 BirthDeath Processes; 1.3 Grasshopper and Kangaroo Movement; 1.4 Velocity Jump Process; 1.5 Size of Cells in a Single Line; 1.6 TwoPhase Cell Cycle Model; 1.7 Stochastic Billiard as a Cell Cycle Model; 1.8 Stochastic Gene Expression I; 1.9 Stochastic Gene Expression II; 1.10 Gene Regulatory Models with Bursting; 1.11 Neural Activity; 1.12 Processes with Extra Jumps on a Subspace; 1.13 SizeStructured Population Model; 1.14 AgeStructured Population Model; 1.15 Asexual Phenotype Population Model
 1.16 Phenotype Model with a Sexual Reproduction1.17 CoagulationFragmentation Process in a Phytoplankton Model; 1.18 Paralog Families; 1.19 Definition of PDMP;
 2 Markov Processes; 2.1 Transition Probabilities and Kernels; 2.1.1 Basic Concepts; 2.1.2 Transition Operators; 2.1.3 Substochastic and Stochastic Operators; 2.1.4 Integral Stochastic Operators; 2.1.5 Frobenius
 Perron Operator; 2.1.6 Iterated Function Systems; 2.2 DiscreteTime Markov Processes; 2.2.1 Markov Processes and Transition Probabilities; 2.2.2 Random Mapping Representations; 2.2.3 Canonical Processes
 2.3 ContinuousTime Markov Processes2.3.1 Basic Definitions; 2.3.2 Processes with Stationary and Independent Increments; 2.3.3 Markov JumpType Processes; 2.3.4 Generators and Martingales; 2.3.5 Existence of PDMPs; 2.3.6 Transition Functions and Generators of PDMPs;
 3 Operator Semigroups; 3.1 Generators and Semigroups; 3.1.1 Essentials of Banach Spaces and Operators; 3.1.2 Definitions and Basic Properties; 3.1.3 The Resolvent; 3.2 Basic Examples of Semigroups; 3.2.1 Uniformly Continuous Semigroups; 3.2.2 Multiplication Semigroups; 3.2.3 Translation Semigroups
 3.3 Generators of Contraction Semigroups3.3.1 The Hille
 Yosida Theorem; 3.3.2 The Lumer
 Phillips Theorem; 3.3.3 Perturbations of Semigroups; 3.3.4 Perturbing Boundary Conditions;
 4 Stochastic Semigroups; 4.1 Aspects of Positivity; 4.1.1 Positive Operators; 4.1.2 Substochastic Semigroups; 4.1.3 Resolvent Positive Operators; 4.1.4 Generation Theorems; 4.1.5 Positive Perturbations; 4.1.6 Positive Unbounded Perturbations; 4.1.7 Adjoint and Transition Semigroups; 4.2 Stochastic Semigroups for PDMPs; 4.2.1 JumpType Markov Processes; 4.2.2 Semigroups for Semiflows; 4.2.3 PDMPs Without Boundaries
16. Random walks and heat kernels on graphs [2017]
 Barlow, M. T., author.
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, [2017]
 Description
 Book — xi, 226 pages : illustrations ; 23 cm.
 Summary

 Preface
 1. Introduction
 2. Random walks and electrical resistance
 3. Isoperimetric inequalities and applications
 4. Discrete time heat kernel
 5. Continuous time random walks
 6. Heat kernel bounds
 7. Potential theory and Harnack inequalities Appendix A References Index.
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QA274.73 .B3735 2017  Unknown 
17. Random walks and heat kernels on graphs [2017]
 Barlow, M. T.
 Cambridge : Cambridge University Press, [2017]
 Description
 Book — online resource (xii, 226 pages) : illustrations
 Summary

 Random walks and electrical resistance
 Isoperimetric inequalities and applications
 Discrete time heat kernel
 Continuous time random walks
 Heat kernel bounds
 Potential Theory and harnack inequalities
 Online
Medical Library (Lane)
Medical Library (Lane)  Status 

Check Lane Library catalog for status  
CAMBRIDGE  Unknown 
 Chinaei, Hamiza, author.
 Cham : Springer, 2016.
 Description
 Book — 1 online resource.
 Summary

 1 Introduction
 2 A few words on topic modeling
 3 Sequential decision making in spoken dialog management
 4 Learning the dialog POMDP model components
 5 Learning the reward function
 6 Application on healthcare dialog management
 7 Conclusions and future work.
 Zucchini, W.
 Second edition.  Boca Raton : CRC Press, Taylor & Francis Group, [2016]
 Description
 Book — 1 online resource : text file, PDF.
 Summary

 Model structure, properties and methodsPreliminaries: mixtures and Markov chainsIntroductionIndependent mixture modelsMarkov chainsExercises Hidden Markov models: definition and propertiesA simple hidden Markov modelThe basicsThe likelihoodExercises Direct maximization of the likelihoodIntroductionScaling the likelihood computationMaximization subject to constraintsOther problemsExample: earthquakesStandard errors and confidence intervalsExample: parametric bootstrapExercises Estimation by the EM algorithmForward and backward probabilitiesThe EM algorithmExamples of EM applied to PoissonHMMsDiscussionExercises Forecasting, decoding and state predictionConditional distributionsForecast distributionsDecodingState predictionHMMs for classificationExercises Model selection and checkingModel selection by AIC and BICModel checking with pseudoresidualsExamplesDiscussionExercises Bayesian inference for PoissonHMMsApplying the Gibbs sampler to PoissonHMMsBayesian estimation of the number of statesExample: earthquakesDiscussionExercises R packagesThe package depmixS4The package HiddenMarkovThe package msmThe package R20penBUGSDiscussion ExtensionsGeneral statedependent distributionsIntroductionUnivariate statedependent distributionMultinomial and categorical HMMsMultivariate statedependent distributionExercises Covariates and other extra dependenciesIntroductionHMMs with covariatesHMMs based on a secondorder Markox chainHMMs with other additional dependenciesExercises Continuousvalued state processesIntroductionModels with continousvalued state processFitting an SSM to the earthquake dataDiscussion Hidden semiMarkov models as HMMsIntroductionSemiMarkov processes, hidden semiMarkov models and approximating HMMsExamples of HSMMs as HMMsGeneral HSMMR codeSome examples of dwelltime distributionsFitting HSMMs via the HMM representationExample: earthquakesDiscussionExercises HMMs for longitudinal dataIntroductionSome parameters constant across componentsModels with random effectsDiscussionExercises Applications Introduction to applications Epileptic seizuresIntroductionModels fittedModel checking by pseudoresidualsExercises Daily rainfall occurrenceIntroductionModels fitted Eruptions of the Old Faithful geyserIntroductionThe dataBinary time series of short and long eruptionsNormalHMMs for durations and waiting timesBivariate model for durations and waiting timesExercises HMMs for animal movementIntroductionDirectional dataHMMs for movement dataBasic HMM for Drosophila movementHMMs and HSMMs for bison movementMixed HMMs for woodpecker movementExercises Wind direction at KoebergIntroductionWind direction classified into
 16 categoriesWind direction as a circular variableExercises Models for financial seriesMultivariate HMM for returns on four sharesStochastic volatility modelsExercises Births at Edendale HospitalIntroductionModels for the proportion CaesareanModels for the total number of deliveriesConclusion Homicides and suicides in Cape TownIntroductionFirearm homicides as a proportion of all homicides, suicides and legal intervention homicidesThe number of firearm homicidesFirearm homicide and suicide proportionsProportion in each of the five categories Animal behaviour model with feedbackIntroductionThe modelLikelihood evaluationParameter estimation by maximum likelihoodModel checkingInferring the underlying stateModels for a heterogeneous group of subjectsOther modifications or extensionsApplication to caterpillar feeding behaviourDiscussion Survival rates of Soay sheepIntroductionMRR data without use of covariatesMRR data involving covariate informationApplication to Soay sheep dataConclusion Examples of R codeThe functionsExamples of code using the above functions Some proofsFactorization needed for forward probabilitiesTwo results for backward probabilitiesConditional independence of Xt1 and XTt+1 References Author index Subject index.
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 Yu, ShunZheng, author.
 Amsterdam : Elsevier, [2016]
 Description
 Book — ix, 195 pages : illustrations ; 23 cm
 Summary

Hidden semiMarkov models (HSMMs) are among the most important models in the area of artificial intelligence / machine learning. Since the first HSMM was introduced in 1980 for machine recognition of speech, three other HSMMs have been proposed, with various definitions of duration and observation distributions. Those models have different expressions, algorithms, computational complexities, and applicable areas, without explicitly interchangeable forms. Hidden SemiMarkov Models: Theory, Algorithms and Applications provides a unified and foundational approach to HSMMs, including various HSMMs (such as the explicit duration, variable transition, and residential time of HSMMs), inference and estimation algorithms, implementation methods and application instances. Learn new developments and stateoftheart emerging topics as they relate to HSMMs, presented with examples drawn from medicine, engineering and computer science. * Discusses the latest developments and emerging topics in the field of HSMMs* Includes a description of applications in various areas including, Human Activity Recognition, Handwriting Recognition, Network Traffic Characterization and Anomaly Detection, and Functional MRI Brain Mapping.* Shows how to master the basic techniques needed for using HSMMs and how to apply them.
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QA274.7 .Y8 2016  Unknown 
 De Saporta, Benoîte, author.
 London, UK : ISTE Ltd ; Hoboken, NJ : John Wiley & Sons, Inc., 2016.
 Description
 Book — xiv, 279 pages : illustrations ; 24 cm.
 Summary

 Preface ix Introduction xi
 Part 1. Piecewise Deterministic Markov Processes and Quantization
 1
 Chapter 1. Piecewise Deterministic Markov Processes
 3 1.1. Introduction
 3 1.2. Notation
 4 1.3. Definition of a PDMP
 5 1.4. Regularityassumptions
 8 1.4.1. Lipschitz continuity along the flow
 8 1.4.2. Regularity assumptions on the local characteristics
 9 1.5. Timeaugmentedprocess
 11 1.6. EmbeddedMarkovchain
 15 1.7. Stopping times
 16 1.8. ExamplesofPDMPs
 20 1.8.1. Poisson processwith trend
 20 1.8.2. TCP
 21 1.8.3. Air conditioningunit
 22 1.8.4. Crack propagationmodel
 23 1.8.5. Repairworkshopmodel
 24
 Chapter 2. Examples in Reliability
 27 2.1. Introduction
 27 2.2. Structure subject to corrosion
 28 2.2.1. PDMPmodel
 29 2.2.2. Deterministic time to reach the boundary
 32 2.3. The heatedholduptank
 33 2.3.1. Tank dynamics
 34 2.3.2. PDMPmodel
 36
 Chapter 3. Quantization Technique
 39 3.1. Introduction
 39 3.2. Optimal quantization
 40 3.2.1. Optimal quantization of a random variable
 40 3.2.2. Optimal quantization of a Markovchain
 42 3.3. SimulationofPDMPs
 44 3.3.1. Simulation of timedependent intensity
 45 3.3.2. Simulation of trajectories
 45 3.4. QuantizationofPDMPs
 47 3.4.1. Scale of coordinates of the state variable
 48 3.4.2. Cardinality of the mode variable
 50
 Part 2. Simulation of Functionals
 53
 Chapter 4. Expectation of Functionals
 55 4.1. Introduction
 55 4.2. Recursive formulation
 57 4.2.1. Lipschitz continuity
 58 4.2.2. Iterated operator
 60 4.2.3. Approximationscheme
 61 4.3. Lipschitz regularity
 62 4.4. Rate of convergence
 69 4.5. Timedependent functionals
 71 4.6. Deterministic time horizon
 74 4.6.1. Direct estimation of the running cost term
 74 4.6.2. Bounds of the boundary jump cost term
 77 4.6.3. Bounds in the general case
 79 4.7. Example
 81 4.8. Conclusion
 84
 Chapter 5. Exit Time
 87 5.1. Introduction
 87 5.2. Problem setting
 88 5.2.1. Distribution
 90 5.2.2. Moments
 91 5.2.3. Computationhorizon
 92 5.3. Approximationschemes
 92 5.4. Convergence
 95 5.4.1. Distribution
 95 5.4.2. Moments
 100 5.5. Example
 101 5.6. Conclusion
 108
 Chapter 6. Example in Reliability: Service Time
 109 6.1. Mean thickness loss
 109 6.2. Service time
 112 6.2.1. Mean service time
 114 6.2.2. Distribution of the service time
 118 6.3. Conclusion
 121
 Part 3. Optimization
 123
 Chapter 7. Optimal Stopping
 125 7.1. Introduction
 125 7.2. Dynamic programming equation
 128 7.3. Approximation of the value function
 130 7.4. Lipschitz continuity properties
 132 7.4.1. Lipschitz properties of J and K
 132 7.4.2. Lipschitz properties of the value functions
 135 7.5. Error estimation for the value function
 138 7.5.1. Second term
 140 7.5.2. Third term
 141 7.5.3. Fourth term
 147 7.5.4. Proof of theorem 7.1
 148 7.6. Numerical construction of an [1]optimal stopping time
 149 7.7. Example
 161
 Chapter 8. Partially Observed Optimal Stopping Problem
 165 8.1. Introduction
 165 8.2. Problem formulation and assumptions
 167 8.3. Optimal filtering
 170 8.4. Dynamicprogramming
 175 8.4.1. Preliminaryresults
 176 8.4.2. Optimal stopping problem under complete observation
 180 8.4.3. Dynamic programming equation
 181 8.5. Numerical approximation by quantization
 188 8.5.1. Lipschitz properties
 189 8.5.2. Discretization scheme
 195 8.5.3. Numerical construction of an [1]optimal stopping time
 205 8.6. Numerical example
 211
 Chapter 9. Example in Reliability: Maintenance Optimization
 215 9.1. Introduction
 215 9.2. Corrosionprocess
 216 9.3. Air conditioningunit
 219 9.4. The heatedholduptank
 221 9.4.1. Problem setting and simulation
 222 9.4.2. Numerical results and validation
 224 9.5. Conclusion
 228
 Chapter 10. Optimal Impulse Control
 231 10.1. Introduction
 231 10.2. Impulse controlproblem233 10.3. Lipschitzcontinuity properties
 236 10.3.1. Lipschitz properties of the operators
 236 10.3.2. Lipschitz properties of the operator L
 239 10.4. Approximation of the value function
 242 10.4.1. Time discretization
 245 10.4.2. Approximation of the value functions on the control grid U
 246 10.4.3. Approximation of the value function
 255 10.4.4. Stepbystep description of the algorithm
 259 10.4.5. Practical implementation
 259 10.5. Example
 262 10.6. Conclusion
 264 Bibliography
 269 Index 277.
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QA274.7 .D45 2016  Unknown 
 Krishnamurthy, V. (Vikram) author.
 Cambridge, United Kingdom : Cambridge University Press, 2016.
 Description
 Book — xiii, 476 pages : illustrations ; 26 cm
 Summary

 Preface
 1. Introduction Part I. Stochastic Models and Bayesian Filtering:
 2. Stochastic statespace models
 3. Optimal filtering
 4. Algorithms for maximum likelihood parameter estimation
 5. Multiagent sensing: social learning and data incest Part II. Partially Observed Markov Decision Processes. Models and Algorithms:
 6. Fully observed Markov decision processes
 7. Partially observed Markov decision processes (POMDPs)
 8. POMDPs in controlled sensing and sensor scheduling Part III. Partially Observed Markov Decision Processes:
 9. Structural results for Markov decision processes
 10. Structural results for optimal filters
 11. Monotonicity of value function for POMPDs
 12. Structural results for stopping time POMPDs
 13. Stopping time POMPDs for quickest change detection
 14. Myopic policy bounds for POMPDs and sensitivity to model parameters Part IV. Stochastic Approximation and Reinforcement Learning:
 15. Stochastic optimization and gradient estimation
 16. Reinforcement learning
 17. Stochastic approximation algorithms: examples
 18. Summary of algorithms for solving POMPDs Appendix A. Short primer on stochastic simulation Appendix B. Continuoustime HMM filters Appendix C. Markov processes Appendix D. Some limit theorems Bibliography Index.
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QA274.7 .K75 2016  Unknown 
 Probability on Algebraic and Geometric Structures (Conference) (2014 : Carbondale, Illinois)
 Providence, Rhode Island : American Mathematical Society, [2016]
 Description
 Book — ix, 221 pages ; 26 cm.
 Summary

 * A. Anckar and G, Hognas, The fine structure of the stationary distribution for a simple Markov process* D. Bell, Superdegenerate hypoelliptic differential operators* G. Budzban and A. Mukherjea, Some remarks on the convolution equation $\mu*\beta=\mu$ and product semigroups* S. Chakraborty, Limit distributions of products of i.i.d. random $2x2$ stochastic matrices: An open problem* A. Cosso, C. Di Girolami, and F. Russo, Calculus via regularizations in Banach spaces and Kolmogorovtype pathdependent equations* P. Feinsilver, Matrices with zero row sums, tree theorems and Markov chain on trees* P. Graczyk and P. Sawyer, Convolution of orbital measures on symmetric spaces: A survey* G. Hognas and B. Jung, Exit times for some autoregressive processes with nonGaussian noise distributions* I. KemajouBrown, Brief history of optimal control theory and some recent developments* J. Kocik, Krawtchouk matrices, Feynman path integral and the split quaternions* R. Leandre, The ItoStratonovich formula for an operator of order four* C. R. E. Raja and R. Schott, Random walks on motion groups* H. Schurz and A. Talafha, Existence, uniqueness, and energy of modified stochastic sineGordon equation with multiplicative noise on onedimensional domain* L. Siriwardena and H. R. Hughes, Squared Bessel process with delay* G. S. Staples, Kravchuk matrices and induced operators on Clifford algebras.
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QA273.6 .P745 2014  Unknown 
 ZúñigaGalindo, W. A. author.
 Cham, Switzerland : Springer, [2016]
 Description
 Book — xvi, 175 pages ; 24 cm.
 Summary

 pAdic Analysis: Essential Ideas and Results. Parabolictype Equations and Markov Processes. NonArchimedean Parabolictype Equations With Variable Coefficients. ParabolicType Equations on Adeles. Fundamental Solutions and Schrodinger Equations. Pseudodifferential Equations of KleinGordon Type.
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Shelved by Series title V.2174  Unknown 
 Bacallado, Sergio, author.
 Stanford, Calif. : Department of Statistics, Stanford University, March 2015.
 Description
 Book — 26 pages ; 28 cm.
Special Collections
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260494  Unavailable In process 
26. Markov processes [2015]
 Kirkwood, James R., author.
 Boca Raton, FL : CRC Press, [2015]
 Description
 Book — xii, 327 pages : illustrations ; 24 cm.
 Summary

 Review of Probability Short History Review of Basic Probability Definitions Some Common Probability Distributions Properties of a Probability Distribution Properties of the Expected Value Expected Value of a Random Variable with Common Distributions Generating Functions Moment Generating Functions Exercises DiscreteTime, FiniteState Markov Chains Introduction Notation Transition Matrices Directed Graphs: Examples of Markov Chains Random Walk with Reflecting Boundaries Gamblera (TM)s Ruin Ehrenfest Model Central Problem of Markov Chains Condition to Ensure a Unique Equilibrium State Finding the Equilibrium State Transient and Recurrent States Indicator Functions PerronFrobenius Theorem Absorbing Markov Chains Mean First Passage Time Mean Recurrence Time and the Equilibrium State Fundamental Matrix for Regular Markov Chains Dividing a Markov Chain into Equivalence Classes Periodic Markov Chains Reducible Markov Chains Summary Exercises DiscreteTime, InfiniteState Markov Chains Renewal Processes Delayed Renewal Processes Equilibrium State for Countable Markov Chains Physical Interpretation of the Equilibrium State Null Recurrent versus Positive Recurrent States Difference Equations Branching Processes Random Walk in Exercises Exponential Distribution and Poisson Process Continuous Random Variables Cumulative Distribution Function (Continuous Case) Exponential Distribution o(h) Functions Exponential Distribution as a Model for Arrivals Memoryless Random Variables Poisson Process Poisson Processes with Occurrences of Two Types Exercises ContinuousTime Markov Chains Introduction Generators of Continuous Markov Chains: The Kolmogorov Forward and Backward Equations Connection Between the Steady State of a Continuous Markov Chain and the Steady State of the Embedded Matrix Explosions Birth and BirthDeath Processes Birth and Death Processes Queuing Models Detailed Balance Equations Exercises Reversible Markov Chains Random Walks on Weighted Graphs DiscreteTime BirthDeath Process as a Reversible Markov Chain ContinuousTime Reversible Markov Chains Exercises Bibliography.
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QA274.7 .K58 2015  Unknown 
27. Measuring sample quality with Stein's method [2015]
 Gorham, Jackson, author.
 Stanford, Calif. : Department of Statistics, Stanford University, September 2015.
 Description
 Book — 28 pages ; 28 cm.
Special Collections
Special Collections  Status 

University Archives  
260508  Unavailable In process 
 Bovier, Anton, 1957 author.
 Cham : Springer, [2015]
 Description
 Book — xxi, 581 pages : illustrations (some color) ; 25 cm.
 Summary

 Introduction
 Background and Motivation
 Phenomenology
 Condensation and magnetisation : from gases to ferromagnets
 Historical perspective
 Early achievements
 The pathwise approach
 The spectral approach
 The potentialtheoretic approach
 The computational approach
 Aims and Scopes
 Two paradigmatic models
 Kramers model : Brownian motion in a doublewell
 Finitestate Markov processes
 Model reduction
 Variational point of view
 Specific models
 Related topics
 Markov Processes
 Some Basic Notions from Probability Theory
 Probability and measures
 Probability spaces
 Random variables
 Integrals
 Spaces of integrable functions
 Convergence
 RadonNikodým derivative
 Stochastic processes
 Definition of stochastic processes
 The DaniellKolmogorov extension theorem
 Conditional expectations
 Definition of conditional expectations
 Elementary properties of conditional expectations
 Conditional probability measures
 Martingales in discrete time
 Definitions
 Upcrossings and convergence
 Maximum inequalities
 Stopping times and stopped martingales
 Martingales in continuous time
 Càdlàg functions
 Filtrations, supermartingales and càdlàg processes
 The Doob regularity theorem
 Convergence theorems and martingale inequalities
 Stopping times
 First hitting time and first entrance time
 Optional stopping and optional sampling
 Bibliographical notes
 Markov Processes in Discrete Time
 Markov processes : main definitions and key facts
 Definition and elementary properties
 Markov processes with stationary transition probabilities
 The strong Markov property
 Markov processes and martingales
 Semigroups
 The martingale problem
 Harmonic functions and martingales
 The Doob transform
 Markov processes with countable state space
 Bibliographical notes
 Markov Processes in Continuous Time
 Markov jump processes
 Brownian motion
 Definition of Brownian motion
 Martingale and Markov properties
 General Markov processes
 Semigroups and generators
 FellerDynkin processes
 The strong Markov property
 The martingale problem
 Generators and cores
 The martingale problem
 Uniqueness
 Existence
 Itō calculus
 Squareintegrable continuous martingales
 Stochastic integrals for simple processes
 Itō formula
 Stochastic differential equations
 Strong solutions
 Existence and uniqueness of strong solutions
 The Doob transform
 The Girsanov theorem
 Stochastic partial differential equations
 The stochastic AllenCahn equation
 Discretisation
 Bibliographical notes
 Large Deviations
 Large deviation principles
 Path large deviations for diffusion processes
 Brownian motion
 Brownian motion with drift
 Diffusion processes
 Path large deviations for stochastic partial differential equations
 Path large deviations for Markov processes
 FreidlinWentzell theory
 Properties of action functional
 Crossing and exit problems
 Metastability
 Bibliographical notes
 Potential Theory
 The Dirichlet problem : discrete time
 Definition
 Green function, equilibrium potential and measure
 Reversibility
 Onedimensional nearestneighbour random walks
 The Dirichlet problem : continuous time
 Definition
 Countable state space
 Diffusion processes
 Reversible Markov processes
 Onedimensional diffusions
 Variational principles
 The Dirichlet principle
 The Thomson principle
 The BermanKonsowa principle
 Variational principles in the nonreversible setting
 Bibliographical notes
 Metastability
 Key Definitions and basic properties
 Characterisation of metastability
 Renewal estimates and ultrametricity
 Estimates on mean hitting times
 Rough bounds
 Sharp bounds
 Spectral characterisation of metastability
 A priori bounds
 Characterisation of small eigenvalues
 Computation of small eigenvalues
 Exponential law of the metastable exit times
 Metastability in uncountable state spaces
 Bibliographical notes
 Basic techniques
 Capacity estimates
 General strategies
 Lower bounds via flows
 Coarsegraining
 Lumping
 Regularity estimates
 Elliptic regularity theory
 Coupling methods
 Bibliographical notes
 Applications : diffusions with small noise
 Discrete reversible diffusions
 Definitions
 Upper bounds on capacities
 Cleaning of the Dirichlet form
 Construction of an approximate harmonic function
 Final estimate
 Lower bounds on capacities
 Bibliographical notes
 Diffusion Processes with Gradient Drift
 The setting
 Capacity estimates and mean hitting times
 Main results
 Rough estimates on capacities and harmonic functions
 Sharp estimates on capacities
 Metastable exit times and capacities
 Spectral theory
 Main results
 A priori spectral estimates
 Principal Dirichlet eigenvalues
 Exponentially small eigenvalues and their eigenfunctions
 Improved error estimates
 Exponential distribution of metastable exit times
 Bibliographical notes
 Stochastic Partial Differential Equations
 Definitions, main theorem and outline of proof
 Approximation properties of the potential
 Estimate of the capacity
 Properties of the potential
 Upper bound
 Lower bound
 Estimate of the equilibrium potential
 Proof of the main theorem
 Bibliographical notes
 Applications : coarsegraining in large volumes at positive temperatures
 The CurieWeiss model
 The CurieWeiss model
 Metastable behaviour
 Bibliographical notes
 The CurieWeiss model with a random magnetic field : discrete distributions
 The model
 Gibbs measure and order parameter
 Glauber dynamics
 Coarsegraining
 The landscape near critical points
 Eigenvalues of the Hessian
 Topology of the landscape
 Bibliographical notes
 The CurieWeiss Model with random magnetic field : continuous distributions
 Main results
 Coarsegraining and the mesoscopic approximation
 Coarsegraining
 The energy landscape near critical points
 Upper bounds on capacities
 Lower bounds on capacities
 Twoscale flows
 Propagation of errors along microscopic paths
 Estimates on mean hitting times
 Mean hitting time and equilibrium potential
 Upper bounds on harmonic functions
 Bibliographical notes
 Applications : lattice systems in small volumes at low temperatures
 Abstract setup and metastability in the zerotemperature limit
 Hypotheses and universal metastability theorems
 Metropolis dynamics and geometric definitions
 Metastability theorems and hypotheses
 Discussion
 Consequences of the hypotheses
 Preliminaries
 Dirichlet form and capacity
 A priori estimates on the capacity
 Graph structure of the energy landscape
 Metastable pair
 Proof of the metastability theorems
 Exponential distribution of the crossover time
 Average crossover time
 Gate for the crossover and uniform entrance distribution
 Beyond Metropolis dynamics
 Heatbath dynamics
 Probabilistic cellular automata
 Bibliographical notes
 Glauber Dynamics
 Introduction and main results
 Model
 Metastable regime and critical droplet size
 Main theorems
 Discussion
 Geometric definitions
 Verification of the two hypotheses
 First hypothesis
 Second hypothesis
 Structure of the communication level set
 Computation of the prefactor
 Extension to three dimensions
 Bibliographical notes
 Kawasaki dynamics
 Introduction and main results
 Model
 Metastable regime and critical droplet size
 Main theorems
 Discussion
 Geometric definitions
 Verification of the two hypotheses
 First hypothesis
 Second hypothesis
 Structure of the communication level set
 Canonical protocritical droplets
 Protocritical and critical droplets
 Identification of the protocritical and the critical set
 Motion on the plateau
 Cardinality of the set of protocritical droplets
 Asymptotics of the prefactor for large volumes
 Geometry of critical droplets and wells
 Capacity bounds on the prefactor
 Capacity asymptotics
 Extension to three dimensions
 Bibliographical notes
 Applications : lattice systems in large volumes at low temperatures
 Glauber dynamics
 Introduction and main results
 Glauber dynamics in large volumes
 Main theorem
 Discussion
 Average time to create a critical droplet
 Estimate of the equilibrium potential
 Estimate of the capacity
 Average time to go beyond the critical droplet
 Estimate of the equilibrium potential
 Estimate of the capacity
 Average time to grow a droplet twice the critical size
 Estimate of the equilibrium potential
 Estimate of the capacity
 Sparseness of subcritical droplets
 Typicality of starting configurations
 Bibliographical notes
 Kawasaki dynamics
 Introduction and main results
 Kawasaki dynamics in large volumes
 Main theorem
 Discussion
 Average time to create a critical droplet
 Estimate of the equilibrium potential
 Estimate of the capacity
 Average time to grow a droplet twice the critical size
 Equivalence of ensembles
 Partition functions for different numbers of particles
 Partition functions for different volumes
 Atypicality of critical droplets
 Typicality of starting configurations
 The critical droplet is the threshold
 Bibliographical notes
 Applications : lattice systems in small volumes at high densities
 The zerorange process
 Model and basic properties
 Metastable behaviour
 Finite system size
 Diverging system size
 Capacity estimates
 Lowerbound
 Upper bound
 Proof of the main theorems
 Finite system size
 Diverging system size
 Proof that the condensate configurations form a metastable set
 Bibliographical notes
 Challenges
 Challenges within metastability
 Glauber dynamics in large volumes at small magnetic fields
 Metastable crossover time
 Wulff construction
 Heuristics
 Crystallisation in small volumes at low temperatures
 Static model
 Dynamic model
 Metastability theorems for the soft disk potential
 Extension to other pair potentials
 Bibliographical notes
 Challenges beyond metastability
 Low temperatures
 Small magnetic fields
 Bibliographical notes
 Glossary
 References
 Index.
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QA402 .B685 2015  Unknown 
 Tatarinova, Tatiana V., author.
 London : Imperial College Press, [2015]
 Description
 Book — xxv, 269 pages : illustrations (some color) ; 24 cm
 Summary

 Introduction Mathematical Description of Nonlinear Mixture Models Label Switching and Trapping Treatment of Mixture Models with an Unknown Number of Components Applications of BDMCMC, KLMCMC Bayesian Clustering Methods.
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QA274.7 .T38 2015  Unknown 
 Tatarinova, Tatiana V., author.
 Hackensack, NJ : Imperial College Press, [2015]
 Description
 Book — 1 online resource (xxiv, 269 pages) : illustrations
 Summary

 Introduction Mathematical Description of Nonlinear Mixture Models Label Switching and Trapping Treatment of Mixture Models with an Unknown Number of Components Applications of BDMCMC, KLMCMC Bayesian Clustering Methods.
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31. Optimization of stochastic discrete systems and control on complex networks : computational networks [2015]
 Lozovanu, Dmitrii, author.
 Cham : Springer, 2015.
 Description
 Book — 1 online resource (xix, 400 pages) : illustrations.
 Summary

 Discrete stochastic processes, numerical methods for Markov chains and polynomial time algorithms. Stochastic optimal control problems and Markov decision processes with infinite time horizon. A gametheoretical approach to Markov decision processes, stochastic positional games and multicriteria control models. Dynamic programming algorithms for finite horizon control problems and Markov decision processes.
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 Owen, Art B., author.
 Stanford, Calif. : Department of Statistics, Stanford University, November 2015.
 Description
 Book — 12 pages ; 28 cm.
Special Collections
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260511  Unavailable In process 
 Bakry, D. (Dominique), author.
 Cham ; New York : Springer, [2014]
 Description
 Book — xx, 552 pages ; 25 cm.
 Summary

 Markov semigroups, basics and examples
 Markov semigroups
 Markov processes and associated semigroups
 Markov semigroups, invariant measures and kernels
 ChapmanKolmogorov equations
 Infinitesimal generators and Carré du Champ operators
 FokkerPlanck equations
 Symmetrie Markov semigroups
 Dirichlet forms and spectral decompositions
 Ergodicity
 Markov chains
 Stochastic differential equations and diffusion processes
 Diffusion semigroups and operators
 Ellipticity and hypoellipticity
 Domains
 Summary of hypotheses (Markov semigroup)
 Working with Markov semigroups
 Curvaturedimension condition
 Notes and references
 Model examples
 Euclidean heat semigroup
 Spherical heat semigroup
 Hyperbolic heat semigroup
 The heat semigroup on a halfline and the Bessel semigroup
 The heat semigroup on the circle and on a bounded interval
 SturmLiouville aemigroups on an interval
 Diffusion semigroups associated with orthogonal polynomials
 Notes and references
 Symmetric Markov diffusion operators
 Markov triples
 Second order differential operators on a manifold
 Heart of darkness
 Summary of hypotheses (Markov triple)
 Notes and references
 Three model functional inequalities
 Poincaré inequalities
 The example of the OrnsteinUhlenbeck semigroup
 Poincaré inequalities
 Tensorization of Poincaré inequalities
 The example of the exponential measure, and exponential integrability
 Poincaré inequalities on the real line
 The Lyapunov function method
 Local Poincaré inequalities
 Poincaré inequalities under a curvaturedimension condition
 BrascampLieb inequalities
 Further spectral inequalities
 Notes and references
 Logarithmic Sobolev inequalities
 Logarithmic Sobolev inequalities
 Entropy decay and hypercontractivity
 Integrability of eigenvectors
 Logarithmic Sobolev inequalities and exponential integrability
 Local logarithmic Sobolev inequalities
 Infinitedimensional Harnack inequalities
 Logarithmic Sobolev inequalities under a curvaturedimension condition
 Notes and references
 Sobolev inequalities
 Sobolev inequalities on the model spaces
 Sobolev and related inequalities
 Ultracontractivity and heat kernel bounds
 Ultracontractivity and compact embeddings
 Tensorization of Sobolev inequalities
 Sobolev inequalities and Lipschitz functions
 Local Sobolev inequalities
 Sobolev inequalities under a curvaturedimension condition
 Conformai invariance of Sobolev inequalities
 GagliardoNirenberg inequalities
 Fast diffusion equations and Sobolev inequalities
 Notes and references
 Notes and references
 Related functional, isoperimetric and transportation inequalities
 Generalized functional inequalities
 Inequalities between entropy and energy
 Offdiagonal heat kernel bounds
 Examples
 Beyond nash inequalities
 Weak poincare inequalities
 Further families of functional inequalities
 Summary for the model example ssa
 Notes and references
 Capacity and isoperimetrictype inequalities
 Capacity inequalities and coarea formulas
 Capacity and sobolev inequalities
 Capacity and poincare and logarithmic sobolev inequalities
 Capacity and further functional inequalities
 Gaussian isoperimetrictype inequalities under a curvature condition
 Harnack inequalities revisited
 From concentration to isoperimetry
 Notes and references
 Optimal transportation and functional inequalities
 Optimal transportation
 Transportation cost inequalities
 Transportation proofs of functional inequalities
 HamiltonJacobi equations
 Hypercontractivity of solutions of hamiltonjacobi equations
 Transportation cost and logarithmic sobolev inequalities
 Heat flow contraction in wasserstein space
 Curvature of metrie measure spaces
 Notes and references
 Appendices
 Semigroups of bounded operators on a banach space
 The hilleyosida theory
 Symmetrie operators
 Friedrichs extension of positive operators
 Spectral decompositions
 Essentially selfadjoint operators
 Compact and HilbertSchmidt operators
 Notes and references
 Elements of stochastic calculus
 Brownian motion and stochastic integrals
 The itö formula
 Stochastic differential equations
 Diffusion processes
 Notes and references
 Basic notions in differential and riemannian geometry
 Differentiable manifolds
 Some elementary euclidean geometry
 Basic notions in riemannian geometry
 Riemannian distance
 The riemannian T and T2 operators
 Curvaturedimension conditions
 Notes and references
 Afterword
 Chicken "Gaston Gerard"
 Notation and list of symbols
 Bibliography
 Index.
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QA274.7 .B35 2014  Unknown 
34. Current challenges in stability issues for numerical differential equations : Cetraro, Italy 2011 [2014]
 C.I.M.E. Summer School (2011 : Cetraro, Italy)
 Cham [Switzerland] : Springer, [2014]
 Description
 Book — viii, 313 pages : ill. (some color) ; 24 cm.
 Summary

 Studies on current challenges in stability issues for numerical differential equations / Luca Dieci, Nicola Guglielmi Longterm stability of symmetric partitioned linear multistep methods / Paola Console and Ernst Hairer
 Markov chain Monte Carlo and numerical differential equations / J.M. SanzSerna
 Stability and computation of dynamic patterns in PDEs / WolfJürgen Beyn, Denny Otten, and Jens RottmannMatthes
 Continuous decompositions and coalescing eigenvalues for matrices depending on parameters / Luca Dieci ... [and 3 more]
 Stability of linear problems: joint spectral radius of sets of matrices / Nicola Guglielmi and Marino Zennaro.
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Shelved by Series title V.2082  Unknown 
35. An introduction to Markov processes [2014]
 Stroock, Daniel W., author.
 Second edition.  Heidelberg ; New York : Springer, [2014]
 Description
 Book — xvii, 203 pages ; 25 cm.
 Summary

 Preface. Random Walks, a Good Place to Begin. Doeblin's Theory for Markov Chains. Stationary Probabilities. More about the Ergodic Theory of Markov Chains. Markov Processes in Continuous Time. Reversible Markov Processes. A minimal Introduction to Measure Theory. Notation. References. Index.
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QA274.7 .S765 2014  Unknown 
 Acosta, Alejandro D. de, 1941 author.
 Providence, Rhode Island : American Mathematical Society, 2014.
 Description
 Book — v, 108 pages ; 26 cm.
 Summary

 Introduction The transform kernels Kg and their convergence parameters Comparison of ?(g) and ? ? (g) Proof of Theorem
 1 A characteristic equation and the analyticity of ? f : the case when P has an atom C?S satisfying ? (C)>0 Characteristic equations and the analyticity of ? f: the general case when P is geometrically ergodic Differentiation formulas for u g and ? f in the general case and their consequences Proof of Theorem
 2 Proof of Theorem
 3 Examples Applications to an autoregressive process and to reflected random walk Appendix Background comments References.
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Shelved by Series title NO.1070  Unknown 
 Graham, C. (Carl), author.
 Chichester, West Sussex : John Wiley & Sons, Inc., 2014.
 Description
 Book — 1 online resource (xvi, 232 pages).
 Summary

 Preface ix List of Figures xi Nomenclature xiii Introduction xv
 1 First steps
 1 1.1 Preliminaries
 1 1.2 First properties of Markov chains
 2 1.2.1 Markov chains, finitedimensional marginals, and laws
 2 1.2.2 Transition matrix action and matrix notation
 5 1.2.3 Random recursion and simulation
 9 1.2.4 Recursion for the instantaneous laws, invariant laws
 10 1.3 Natural duality: algebraic approach
 11 1.3.1 Complex eigenvalues and spectrum
 11 1.3.2 Doeblin condition and strong irreducibility
 15 1.3.3 Finite state space Markov chains
 17 1.4 Detailed examples
 21 1.4.1 Random walk on a network
 21 1.4.2 Gambler's ruin
 22 1.4.3 Branching process: evolution of a population
 25 1.4.4 Ehrenfest's Urn
 27 1.4.5 Renewal process
 33 1.4.6 Word search in a character chain
 36 1.4.7 Product chain
 38 Exercises
 40
 2 Past, present, and future
 47 2.1 Markov property and its extensions
 47 2.1.1 Past field, filtration, and translation operators
 47 2.1.2 Markov property
 48 2.1.3 Stopping times and strong Markov property
 50 2.2 Hitting times and distribution
 51 2.2.1 Hitting times, induced chain, and hitting distribution
 51 2.2.2 "One step forward" method, Dirichlet problem
 53 2.3 Detailed examples
 60 2.3.1 Gambler's ruin
 60 2.3.2 Unilateral hitting time for a random walk
 64 2.3.3 Exit time from a box
 67 2.3.4 Branching process
 67 2.3.5 Word search
 71 Exercises
 73
 3 Transience and recurrence
 79 3.1 Sample paths and state space
 79 3.1.1 Communication and closed irreducible classes
 79 3.1.2 Transience and recurrence, recurrent class decomposition
 80 3.1.3 Detailed examples
 83 3.2 Invariant measures and recurrence
 87 3.2.1 Invariant laws and measures
 87 3.2.2 Canonical invariant measure
 89 3.2.3 Positive recurrence, invariant law criterion
 91 3.2.4 Detailed examples
 93 3.3 Complements
 97 3.3.1 Hitting times and superharmonic functions
 97 3.3.2 Lyapunov functions
 99 3.3.3 Time reversal, reversibility, and adjoint chain
 105 3.3.4 Birthanddeath chains
 108 Exercises
 111
 4 Longtime behavior
 119 4.1 Path regeneration and convergence
 119 4.1.1 Pointwise ergodic theorem, extensions
 120 4.1.2 Central limit theorem for Markov chains
 124 4.1.3 Detailed examples
 126 4.2 Longtime behavior of the instantaneous laws
 128 4.2.1 Period and aperiodic classes
 128 4.2.2 Coupling of Markov chains and convergence in law
 132 4.2.3 Detailed examples
 139 4.3 Elements on the rate of convergence for laws
 140 4.3.1 The Hilbert space framework
 140 4.3.2 Dirichlet form, spectral gap, and exponential bounds
 143 4.3.3 Spectral theory for reversible matrices
 146 4.3.4 Continuoustime Markov chains
 149 Exercises
 150
 5 Monte Carlo methods
 155 5.1 Approximate solution of the Dirichlet problem
 155 5.1.1 General principles
 155 5.1.2 Heat equation in equilibrium
 156 5.1.3 Heat equation out of equilibrium
 158 5.1.4 Parabolic partial differential equations
 159 5.2 Invariant law simulation
 162 5.2.1 Monte Carlo methods and ergodic theorems
 162 5.2.2 Metropolis algorithm, Gibbs law, and simulated annealing
 163 5.2.3 Exact simulation and backward recursion
 166 Appendix A Complements
 171 A.1 Basic probabilistic notions
 171 A.1.1 Discrete random variable, expectation, and generating function
 171 A.1.2 Conditional probabilities and independence
 175 A.2 Discrete measure convergence
 177 A.2.1 Total variation norm and maximal coupling
 177 A.2.2 Duality between measures and functions
 180 A.2.3 Weak convergence of laws and convergence in law
 182 A.3 Measuretheoretic framework
 183 A.3.1 Probability spaces
 183 A.3.2 Measurable spaces and functions: signed and nonnegative
 185 A.3.3 Random variables, their laws, and expectations
 186 A.3.4 Random sequences and Kolmogorov extension theorem
 192 References
 195 Solutions for the exercises
 197 Index 229.
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38. Markov chains and dependability theory [2014]
 Rubino, Gerardo, 1955 author.
 Cambridge ; New York : Cambridge University Press, 2014.
 Description
 Book — viii, 278 pages : illustrations ; 26 cm
 Summary

 1. Introduction
 2. Discrete time Markov chains
 3. Continuous time Markov chains
 4. State aggregation of Markov chains
 5. Sojourn times in subsets of states
 6. Occupation times
 7. Performability
 8. Stationary detection
 9. Simulation of dependability models
 10. Bounding techniques.
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QA274.7 .R83 2014  Unknown 
 Providence, Rhode Island : American Mathematical Society, [2014]
 Description
 Book — v, 84 pages ; 25 cm.
 Summary

 Introduction Statement of the results Mixing time preliminaries Outline of the proof of Theorem 2.1 Random graph estimates Supercritical case Subcritical case Critical case Fast mixing of the SwendsenWang process on trees Acknowledgements Bibliography.
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Serials  
Shelved by Series title NO.1092  Unknown 
 Chakraborty, Doran, author.
 Cham : Springer, [2014]
 Description
 Book — 1 online resource (xvii, 147 pages).
 Summary

 Introduction. Background. Learn or Exploit in Adversary Induced Markov Decision Processes. Convergence, Targeted Optimality and Safety in Multiagent Learning. Maximizing. Targeted Modeling of Markovian agents. Structure Learning in Factored MDPs. Related Work. Conclusion and Future Work.
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 Dawson, Donald A. (Donald Andrew), 1937 author.
 Cham [Switzerland] : Springer, [2014]
 Description
 Book — xvii, 856 pages : illustrations ; 24 cm.
 Summary

 Introduction. Emergence and fixation in the FW model with two types. Formulation of the multitype and multiscale model. Formulation of the main results in the general case. A Basic Tool: Dual Representations. Longtime behaviour: ergodicity and nonergodicity. Meanfield emergence and fixation of rare mutants (Phase 1,2). Methods and proofs for the FW model with two types. Emergence, fixation with M =>
 2 lower order types. Emergence, fixation: The general (M, M)type meanfield model. Neutral evolution on E1 after fixation (Phase 3). Reequilibration on higher level E1 (Phase 4). Iteration of the cycle I: Emergence and fixation on E2. Iteration of the cycle  the general multilevel hierarchy. Windingup: Proofs of the Theorems 311.
 Appendix 1  Tightness.
 Appendix 2. Nonlinear semigroup perturbations. References. Index of Notation and Tables of Basic Objects. Index.
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Shelved by Series title V.2092  Unknown 
42. Spectra of symmetrized shuffling operators [2014]
 Reiner, Victor, 1965 author.
 Providence, Rhode Island : American Mathematical Society, 2014.
 Description
 Book — vi, 109 pages : illustrations ; 26 cm.
 Summary

 Introduction Defining the operators The case where O contains only hyperplanes Equivariant theory of BHR random walks The family ? (2 k ,
 1 n?2k) The original family ? (k,
 1 n?k) Acknowledgements Appendix A. G n module decomposition of ? (k,
 1 n?k) Bibliography List of Symbols Index.
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Shelved by Series title NO.1072  Unknown 
43. Continuous average control of piecewise deterministic Markov processes [electronic resource] [2013]
 Costa, Oswaldo Luiz do Valle.
 New York, NY : Springer, c2013.
 Description
 Book — 1 online resource.
 Online

 dx.doi.org SpringerLink
 Google Books (Full view)
 Yin, George, 1954
 2nd ed., [rev. and expanded]  New York : Springer, c2013.
 Description
 Book — xxi, 427 p. : ill. ; 25 cm.
 Summary

 Prologue and preliminaries. Introduction and overview; Introduction; A brief survey: Markov chains: Singular perturbations; Outline of the book ; Mathematical preliminaries; Introduction; Martingales; Markov chains; piecewisedeterministic processes: Construction of Markov chains; Irreducibility and Quasistationary distributions; Gaussian processes and diffusions; Switching diffusions; Notes ; Markovian models; Introduction; Birth and death processes; Finitestate space models: Queues with finite capacity: System reliability: Competing risk theory: Twotimescale Cox processes: Random evolutions: Seasonal variation models; Stochastic optimization problems: Simulated annealing: Continuoustime stochastic approximation: Systems with Markovian disturbances; Linear systems with jump Markov disturbance: Linear Quadratic control problems: Singularly perturbed LQ systems with wideband noise: Largescale systems : decomposition and aggregation; Timescale separation; Notes
 Twotimescale Markov chains. Asymptotic expansions of solutions for forward equations; Introduction; Irreducible case: Asymptotic expansions: Outer expansion: Initiallayer correction: Exponential decay of ...: Asymptotic validation: Examples: Twotimescale expansion; Markov chains with multiple weakly irreducible classes: Asymptotic expansions: Analysis of remainder: Computational procedure : user's guide: Summary of results: An example; Inclusion of absorbing states; Inclusion of transient states; Remarks on countablestatespace cases: Countablestate spaces : Part I: Countablestate spaces : Part II: A remarks on finitedimensional approximation; Remarks on singularly perturbed diffusions; Notes ; Occupation measures : Asymptotic properties and ramification; Introduction; The irreducible case: Occupation measure: Conditions and preliminary results: Exponential bounds: Asymptotic normality: Extensions; Markov chains with weak and strong interactions: Aggregation of Markov chains: Exponential bounds: Asymptotic distributions; Measurable generators; Remarks on inclusion of transient and absorbing states: Inclusion of transient states: Inclusion of absorbing states; Remarks on a stability problem: Notes ; Asymptotic expansions of solutions for backward equations; Introduction; Problem formulation: A preliminary lemma: Formulation; Construction of asymptotic expansions: Leading term ... and zeroorder terminallayer term ...: Higherorder terms; Error estimates; Asymptotic expansions including transient states; Remarks: Related problems; Notes
 Applications : MDPs, nearoptimal controls, numerical methods, and LQG with switching. Markov decision problems; Introduction; Problem formulation; Limit problem; Asymptotic optimality; Convergence rate and error bound; Longrun average cost; Computational procedures; Notes ; Stochastic control of dynamical systems; Introduction; Problem formulation; Properties of the value functions; Asymptotic optimal controls; Convergence rate; Weak convergence approach: Problem setup: Relaxed control formulation: Near optimality; Notes ; Numerical methods for control and optimization; Introduction; Numerical methods for optimal control; Optimization under threshold policy: Stochastic optimization formulation: Convergence: Examples: Error bounds; Notes ; Hybrid LQG problems; Introduction; Problem formulation; Optimal controls; Twotimeseale approximation : recurrent states: Limit riccati equations: Nearly optimal controls; Twotimescale approximation : inclusion of transient states; Twotimescale approximation : inclusion of absorbing states; A numerical example; Remarks on indefinite control weights; Notes ; Background materials; Properties of generators; Weak convergence; Relaxed control; Viscosity solutions of HJB equations; Value functions and optimal controls; Miscellany ; Bibliography ; Index.
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Stacks  
QA274.7 .Y56 2013  Unknown 
 Costa, Oswaldo Luiz do Valle.
 Berlin ; London : Springer, 2013.
 Description
 Book — 1 online resource.
 Summary

 Introduction
 A Few Tools and Notations
 MeanSquare Stability
 Quadratic Optimal Control with Complete Observations
 H₂ Optimal Control with Complete Observations
 Quadratic and H₂ Optimal Control with Partial Observations
 Best Linear Filter with Unknown (x(t), [theta](t))
 H [infinity] Control
 Design Techniques
 Some Numerical Examples.
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 Online

 dx.doi.org SpringerLink
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 Epstein, Charles L., author.
 Princeton, N.J. : Princeton University Press, [2013]
 Description
 Book — 1 online resource(320 p.) : illustrations. Digital: text file; PDF.
 Summary

 Frontmatter
 Contents
 Preface
 Chapter 1. Introduction
 Chapter 2. WrightFisher Geometry
 Chapter 3. Maximum Principles and Uniqueness Theorems
 Chapter 4. The Model Solution Operators
 Chapter 5. Degenerate Hölder Spaces
 Chapter 6. Hölder Estimates for the 1dimensional Model Problems
 Chapter 7. Hölder Estimates for Higher Dimensional Corner Models
 Chapter 8. Hölder Estimates for Euclidean Models
 Chapter 9. Hölder Estimates for General Models
 Chapter 10. Existence of Solutions
 Chapter 11. The Resolvent Operator
 Chapter 12. The Semigroup on ℂ°(P)
 Appendix A: Proofs of Estimates for the Degenerate 1d Model
 Bibliography
 Index.
 Epstein, Charles L.
 Princeton : Princeton University Press, 2013.
 Description
 Book — xiii, 306 pages ; 24 cm.
 Summary

 Preface xi
 1 Introduction
 1 1.1 Generalized Kimura Diffusions
 3 1.2 Model Problems
 5 1.3 Perturbation Theory
 9 1.4 Main Results
 10 1.5 Applications in Probability Theory
 13 1.6 Alternate Approaches
 14 1.7 Outline of Text
 16 1.8 Notational Conventions
 20 I WrightFisher Geometry and the Maximum Principle
 23
 2 WrightFisher Geometry
 25 2.1 Polyhedra and Manifolds with Corners
 25 2.2 Normal Forms and WrightFisher Geometry
 29
 3 Maximum Principles and Uniqueness Theorems
 34 3.1 Model Problems
 34 3.2 Kimura Diffusion Operators on Manifolds with Corners
 35 3.3 Maximum Principles for theHeat Equation
 45 II Analysis of Model Problems
 49
 4 The Model Solution Operators
 51 4.1 The Model Problemin 1dimension
 51 4.2 The Model Problem in Higher Dimensions
 54 4.3 Holomorphic Extension
 59 4.4 First Steps Toward Perturbation Theory
 62
 5 Degenerate Holder Spaces
 64 5.1 Standard Holder Spaces
 65 5.2 WFHolder Spaces in 1dimension
 66
 6 Holder Estimates for the 1dimensional Model Problems
 78 6.1 Kernel Estimates for Degenerate Model Problems
 80 6.2 Holder Estimates for the 1dimensional Model Problems
 89 6.3 Propertiesof the Resolvent Operator
 103
 7 Holder Estimates for Higher Dimensional CornerModels
 107 7.1 The Cauchy Problem
 109 7.2 The Inhomogeneous Case
 122 7.3 The Resolvent Operator
 135
 8 Holder Estimates for Euclidean Models
 137 8.1 Holder Estimates for Solutions in the Euclidean Case
 137 8.2 1dimensional Kernel Estimates
 139
 9 Holder Estimates for General Models
 143 9.1 The Cauchy Problem
 145 9.2 The Inhomogeneous Problem
 149 9.3 Offdiagonal and Longtime Behavior
 166 9.4 The Resolvent Operator
 169 III Analysis of Generalized Kimura Diffusions
 179
 10 Existence of Solutions
 181 10.1 WFHolder Spaces on a Manifold with Corners
 182 10.2 Overview of the Proof
 187 10.3 The Induction Argument
 191 10.4 The Boundary Parametrix Construction
 194 10.5 Solution of the Homogeneous Problem
 205 10.6 Proof of the Doubling Theorem
 208 10.7 The Resolvent Operator and C0Semigroup
 209 10.8 Higher Order Regularity
 211
 11 The Resolvent Operator
 218 11.1 Construction of the Resolvent
 220 11.2 Holomorphic Semigroups
 229 11.3 DiffusionsWhere All Coefficients Have the Same Leading Homogeneity
 230
 12 The Semigroup on C0(P)
 235 12.1 The Domain of the Adjoint
 237 12.2 The Nullspace of L
 240 12.3 Long Time Asymptotics
 243 12.4 Irregular Solutions of the Inhomogeneous Equation
 247 A Proofs of Estimates for the Degenerate 1d Model
 251 A.1 Basic Kernel Estimates
 252 A.2 First Derivative Estimates
 272 A.3 Second Derivative Estimates
 278 A.4 Offdiagonal and Larget Behavior
 291 Bibliography
 301 Index 305.
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Serials  
Shelved by Series title NO.185  Unknown 
 Epstein, Charles L.
 Princeton : Princeton University Press, 2013.
 Description
 Book — 1 online resource. Digital: text file; PDF.
 Summary

 Frontmatter
 Contents
 Preface
 Chapter 1. Introduction
 Chapter 2. WrightFisher Geometry
 Chapter 3. Maximum Principles and Uniqueness Theorems
 Chapter 4. The Model Solution Operators
 Chapter 5. Degenerate Hölder Spaces
 Chapter 6. Hölder Estimates for the 1dimensional Model Problems
 Chapter 7. Hölder Estimates for Higher Dimensional Corner Models
 Chapter 8. Hölder Estimates for Euclidean Models
 Chapter 9. Hölder Estimates for General Models
 Chapter 10. Existence of Solutions
 Chapter 11. The Resolvent Operator
 Chapter 12. The Semigroup on ℂ°(P)
 Appendix A: Proofs of Estimates for the Degenerate 1d Model
 Bibliography
 Index.
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49. Examples in Markov decision processes [2013]
 Piunovskiy, A. B.
 London : Imperial College Press, c2013.
 Description
 Book — xiii, 293 p. : ill. ; 24 cm.
 Summary

 Finite Horizon Models Infinite Horizon Models, Expected Total Loss and Discounted Loss Long Run Average Loss.
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QA274.7 .P58 2013  Unknown 
 Modica, Giuseppe.
 Chichester, West Sussex : John Wiley & Sons Ltd., 2013.
 Description
 Book — 1 online resource (xii, 334 pages)
 Summary

 Preface xi
 1 Combinatorics
 1 1.1 Binomial coefficients
 1 1.1.1 Pascal triangle
 1 1.1.2 Some properties of binomial coefficients
 2 1.1.3 Generalized binomial coefficients and binomial series
 3 1.1.4 Inversion formulas
 4 1.1.5 Exercises
 6 1.2 Sets, permutations and functions
 8 1.2.1 Sets
 8 1.2.2 Permutations
 8 1.2.3 Multisets
 10 1.2.4 Lists and functions
 11 1.2.5 Injective functions
 12 1.2.6 Monotone increasing functions
 12 1.2.7 Monotone nondecreasing functions
 13 1.2.8 Surjective functions
 14 1.2.9 Exercises
 16 1.3 Drawings
 16 1.3.1 Ordered drawings
 16 1.3.2 Simple drawings
 17 1.3.3 Multiplicative property of drawings
 17 1.3.4 Exercises
 18 1.4 Grouping
 19 1.4.1 Collocations of pairwise different objects
 19 1.4.2 Collocations of identical objects
 22 1.4.3 Multiplicative property
 23 1.4.4 Collocations in statistical physics
 24 1.4.5 Exercises
 24
 2 Probability measures
 27 2.1 Elementary probability
 28 2.1.1 Exercises
 29 2.2 Basic facts
 33 2.2.1 Events
 34 2.2.2 Probability measures
 36 2.2.3 Continuity of measures
 37 2.2.4 Integral with respect to a measure
 39 2.2.5 Probabilities on finite and denumerable sets
 40 2.2.6 Probabilities on denumerable sets
 42 2.2.7 Probabilities on uncountable sets
 44 2.2.8 Exercises
 46 2.3 Conditional probability
 51 2.3.1 Definition
 51 2.3.2 Bayes formula
 52 2.3.3 Exercises
 54 2.4 Inclusion exclusion principle
 60 2.4.1 Exercises
 63
 3 Random variables
 68 3.1 Random variables
 68 3.1.1 Definitions
 69 3.1.2 Expected value
 75 3.1.3 Functions of random variables
 77 3.1.4 Cavalieri formula
 80 3.1.5 Variance
 82 3.1.6 Markov and Chebyshev inequalities
 82 3.1.7 Variational characterization of the median and of the expected value
 83 3.1.8 Exercises
 84 3.2 A few discrete distributions
 91 3.2.1 Bernoulli distribution
 91 3.2.2 Binomial distribution
 91 3.2.3 Hypergeometric distribution
 93 3.2.4 Negative binomial distribution
 94 3.2.5 Poisson distribution
 95 3.2.6 Geometric distribution
 98 3.2.7 Exercises
 101 3.3 Some absolutely continuous distributions
 102 3.3.1 Uniform distribution
 102 3.3.2 Normal distribution
 104 3.3.3 Exponential distribution
 106 3.3.4 Gamma distributions
 108 3.3.5 Failure rate
 110 3.3.6 Exercises
 111
 4 Vector valued random variables
 113 4.1 Joint distribution
 113 4.1.1 Joint and marginal distributions
 114 4.1.2 Exercises
 117 4.2 Covariance
 120 4.2.1 Random variables with finite expected value and variance
 120 4.2.2 Correlation coefficient
 123 4.2.3 Exercises
 123 4.3 Independent random variables
 124 4.3.1 Independent events
 124 4.3.2 Independent random variables
 127 4.3.3 Independence of many random variables
 128 4.3.4 Sum of independent random variables
 130 4.3.5 Exercises
 131 4.4 Sequences of independent random variables
 140 4.4.1 Weak law of large numbers
 140 4.4.2 Borel Cantelli lemma
 142 4.4.3 Convergences of random variables
 143 4.4.4 Strong law of large numbers
 146 4.4.5 A few applications of the law of large numbers
 152 4.4.6 Central limit theorem
 159 4.4.7 Exercises
 163
 5 Discrete time Markov chains
 168 5.1 Stochastic matrices
 168 5.1.1 Definitions
 169 5.1.2 Oriented graphs
 170 5.1.3 Exercises
 172 5.2 Markov chains
 173 5.2.1 Stochastic processes
 173 5.2.2 Transition matrices
 174 5.2.3 Homogeneous processes
 174 5.2.4 Markov chains
 174 5.2.5 Canonical Markov chains
 178 5.2.6 Exercises
 181 5.3 Some characteristic parameters
 187 5.3.1 Steps for a first visit
 187 5.3.2 Probability of (at least) r visits
 189 5.3.3 Recurrent and transient states
 191 5.3.4 Mean first passage time
 193 5.3.5 Hitting time and hitting probabilities
 195 5.3.6 Exercises
 198 5.4 Finite stochastic matrices
 201 5.4.1 Canonical representation
 201 5.4.2 States classification
 203 5.4.3 Exercises
 205 5.5 Regular stochastic matrices
 206 5.5.1 Iterated maps
 206 5.5.2 Existence of fixed points
 209 5.5.3 Regular stochastic matrices
 210 5.5.4 Characteristic parameters
 218 5.5.5 Exercises
 220 5.6 Ergodic property
 222 5.6.1 Number of steps between consecutive visits
 222 5.6.2 Ergodic theorem
 224 5.6.3 Powers of irreducible stochastic matrices
 226 5.6.4 Markov chain Monte Carlo
 228 5.7 Renewal theorem
 233 5.7.1 Periodicity
 233 5.7.2 Renewal theorem
 234 5.7.3 Exercises
 239
 6 An introduction to continuous time Markov chains
 241 6.1 Poisson process
 241 6.2 Continuous time Markov chains
 246 6.2.1 Definitions
 246 6.2.2 Continuous semigroups of stochastic matrices
 248 6.2.3 Examples of rightcontinuous Markov chains
 256 6.2.4 Holding times
 259 Appendix A Power series
 261 A.1 Basic properties
 261 A.2 Product of series
 263 A.3 Banach space valued power series
 264 A.3.2 Exercises
 267 Appendix B Measure and integration
 270 B.1 Measures
 270 B.1.1 Basic properties
 270 B.1.2 Construction of measures
 272 B.1.3 Exercises
 279 B.2 Measurable functions and integration
 279 B.2.1 Measurable functions
 280 B.2.2 The integral
 283 B.2.3 Properties of the integral
 284 B.2.4 Cavalieri formula
 286 B.2.5 Markov inequality
 287 B.2.6 Null sets and the integral
 287 B.2.7 Push forward of a measure
 289 B.2.8 Exercises
 290 B.3 Product measures and iterated integrals
 294 B.3.1 Product measures
 294 B.3.2 Reduction formulas
 296 B.3.3 Exercises
 297 B.4 Convergence theorems
 298 B.4.1 Almost everywhere convergence
 298 B.4.2 Strong convergence
 300 B.4.3 Fatou lemma
 301 B.4.4 Dominated convergence theorem
 302 B.4.5 Absolute continuity of integrals
 305 B.4.6 Differentiation of the integral
 305 B.4.7 Weak convergence of measures
 308 B.4.8 Exercises
 312 Appendix C Systems of linear ordinary differential equations
 313 C.1 Cauchy problem
 313 C.1.1 Uniqueness
 313 C.1.2 Existence
 315 C.2 Efficient computation of eQt
 317 C.2.1 Similarity methods
 317 C.2.2 Putzer method
 319 C.3 Continuous semigroups
 321 References
 324 Index 327.
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