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Number of results to display per page
 Arsenʹev, D. G. (Dmitriĭ Germanovich), 1963 author.
 Berlin ; Boston : De Gruyter, [2018]
 Description
 Book — xi, 278 pages ; 25 cm
 Summary

 Introduction: statistical computing algorithms as a subject of adaptive control
 Part I. Evaluation of integrals: Fundamentals of the Monte Carlo method to evaluate definite integrals
 Sequential Monte Carlo method and adaptive integration
 Methods of adaptive integration based on piecewise approximation
 Methods of adaptive integration based on global approximation
 Numerican experiments
 Adaptive importance sampling method based on piecewise constant approximation
 Part II. Solution of integral equations: Semistatistical method of solving integral equations numerically
 Problem of vibration conductivity
 Problem on idealfluid flow around an airfoil
 First basic problem of elasticity theory
 Second basic problem of elasticity theory
 Projectional and statistical method of solving integral equations numerically.
(source: Nielsen Book Data) 9783110554632 20180806
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QA274 .A78 2018  Unknown 
2. Lectures on the Poisson process [2018]
 Last, Günter, author.
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018.
 Description
 Book — xx, 293 pages ; 24 cm.
 Summary

 Preface List of symbols
 1. Poisson and other discrete distributions
 2. Point processes
 3. Poisson processes
 4. The Mecke equation and factorial measures
 5. Mappings, markings and thinnings
 6. Characterisations of the Poisson process
 7. Poisson processes on the real line
 8. Stationary point processes
 9. The Palm distribution
 10. Extra heads and balanced allocations
 11. Stable allocations
 12. Poisson integrals
 13. Random measures and Cox processes
 14. Permanental processes
 15. Compound Poisson processes
 16. The Boolean model and the Gilbert graph
 17. The Boolean model with general grains
 18. Fock space and chaos expansion
 19. Perturbation analysis
 20. Covariance identities
 21. Normal approximation
 22. Normal approximation in the Boolean model Appendix A. Some measure theory Appendix B. Some probability theory Appendix C. Historical notes References Index.
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(source: Nielsen Book Data) 9781107088016 20180115
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QA274.42 .L36 2018  Unknown 
 Duits, Maurice, author.
 Providence, RI : American Mathematical Society, [2018]
 Description
 Book — v, 118 pages ; 24 cm.
 Summary

 Introduction Statement of results Proof of Theorem 2.1 Proof of Theorem 2.3 Asymptotic analysis of $K_n$ and $R_n$ Proof of Proposition 2.4 Proof of Lemma 4.3 Random initial points Proof of Theorem 2.6: the general case Appendix A. Appendix Bibliography.
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(source: Nielsen Book Data) 9781470429645 20181008
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Shelved by Series title NO.1222  Unknown 
4. Random growth models : AMS Short Course Random Growth Models, January 23, 2017, Atlanta, Georgia [2018]
 Providence, Rhode Island : American Mathematical Society, [2018]
 Description
 Book — ix, 256 pages : illustrations ; 26 cm.
 Summary

 Preface / Michael Damron, Firas RassoulAgha, Timo Seppäläinen
 Random growth models : shape and convergence rate / Michael Damron
 Infinite geodesics, asymptotic directions, and Busemann functions in firstpassage percolation / Jack Hanson
 Fluctuations in firstpassage percolation / Philippe Sosoe
 Busemann functions, geodesics, and the competition interface for directed lastpassage percolation / Firas RassoulAgha
 The corner growth model with exponential weights / Timo Seppäläinen
 Exactly solving the KPZ equation / Ivan Corwin.
(source: Nielsen Book Data) 9781470435530 20181029
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QA1 .S95 V.75  Unknown 
5. Stochastic processes : an introduction [2018]
 Jones, P. W. (Peter Watts), 1945 author.
 Third edition.  Boca Raton, FL : CRC Press, Taylor & Francis Group, [2018]
 Description
 Book — xiv, 255 pages ; 25 cm.
 Summary

 Some Background on Probability Some Gambling Problems Random Walks Markov Chains Poisson Processes Birth and Death Processes Queues Reliability and Renewal Branching and Other Random Processes Brownian Motion: Wiener Process. Computer Simulations and Projects Answers and Comments on EndofChapter Problems Appendix References and Further Reading.
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(source: Nielsen Book Data) 9781498778114 20180115
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QA274 .J66 2018  Unknown 
6. XII Symposium of Probability and Stochastic Processes : Merida, Mexico, November 1620, 2015 [2018]
 Symposium of Probability and Stochastic Processes (12th : 2015 : Merida, Mexico)
 Cham, Switzerland : Birkhauser, [2018]
 Description
 Book — xi, 234 pages : color illustrations ; 25 cm.
 Summary

 Scaling limits of MarkovBranching trees and applications. Optimality of twoparameter strategies in stochastic control. Asymptotic results for the severity and surplus before ruin for a class of Levy insurance processes. Characterization of the minimal penalty of a convex risk measure with applications to robust utility maximization for Levy models. BlackwellNash equilibria in zerosum stochastic differential games. A note on Gammaconvergence of monotone functionals. A criterion for blow up in finite time of a system of 1dimensional reactiondiffusion equations. A note on the smalltime behavior of the largest block size of Beta ncoalescents.
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(source: Nielsen Book Data) 9783319776422 20180813
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QA273 .A1 S965 2015  Unknown 
 Löbus, JörgUwe author.
 Providence, Rhode Island : American Mathematical Society, [2017]
 Description
 Book — v, 135 pages ; 26 cm.
 Summary

 Introduction, Basic objects, and main resultFlows and logarithmic derivative relative to $X$ under orthogonal projectionThe density formulaPartial integrationRelative compactness of particle systemsAppendix A. Basic Malliavin calculus for Brownian motion with random initial dataReferencesIndex.
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(source: Nielsen Book Data) 9781470426033 20171023
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Shelved by Series title NO.1185  Unknown 
8. Groups, graphs, and random walks [2017]
 Cambridge : Cambridge University Press, [2017]
 Description
 Book — xvii, 519 pages : illustrations ; 23 cm.
 Summary

 1. Growth of groups and wreath products Laurent Bartholdi
 2. Random walks on some countable groups Alexander Bendikov and Laurent SaloffCoste
 3. The cost of distinguishing graphs Debra Boutin and Wilfried Imrich
 4. A construction of the measurable Poisson boundary  from discrete to continuous groups Sara Brofferio
 5. Structure trees, networks and almost invariant sets Martin J. Dunwoody
 6. Amenability of trees Behrang Forghani and Keivan MallahiKarai
 7. Groupwalk random groups Agelos Georgakopoulos
 8. Ends of branching random walks on planar hyperbolic Cayley graphs Lorenz A. Gilch and Sebastian Muller
 9. Amenability and ergodic properties of topological groups  from Bogolyubov onwards Rostislav Grigorchuk and Pierre de la Harpe
 10. Schreier graphs of Grigorchuk's group and a subshift associated to a nonprimitive substitution Rostislav Grigorchuk, Daniel Lenz and Tatiana Nagnibeda
 11. Thompson's group F is not Liouville Vadim A. Kaimanovich
 12. A proof of the subadditive ergodic theorem Anders Karlsson
 13. Boundaries of Znfree groups Andrei Malyutin, Tatiana Nagnibeda and Denis Serbin
 14. Buildings, groups of Lie type, and random walks James Parkinson
 15. On some random walks driven by spreadout measures Laurent SaloffCoste and Tianyi Zheng
 16. Topics in mathematical crystallography Toshikazu Sunada.
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(source: Nielsen Book Data) 9781316604403 20170911
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QA274.73 .G76 2017  Unknown 
 Riggs, Jamie, author.
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2017.
 Description
 Book — xv, 216 pages ; 26 cm
 Summary

 1. The data sets
 2. The modelbuilding process
 3. Constance variance response models
 4. Nonconstant variance response models
 5. Discrete, categorical response models
 6. Counts response models
 7. Timetoevent response models
 8. Longitudinal response models
 9. Structural equation modeling
 10. Matching data to models.
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(source: Nielsen Book Data) 9781107146990 20170919
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QA276 .R5244 2017  Unknown 
 Papers. Selections
 Skovgaard, Ib M., author.
 Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2017]
 Description
 Book — xvi, 347 pages ; 24 cm
 Online
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QA276 .S5555 2017  Unknown 
11. Nonhomogeneous random walks : Lyapunov function methods for nearcritical stochastic systems [2017]
 Menʹshikov, M. V. (Mikhail Vasilʹevich), author.
 Cambridge, United Kingdom : Cambridge University Press, 2017.
 Description
 Book — xviii, 363 pages : illustrations ; 24 cm.
 Summary

 1. Introduction
 2. Semimartingale approach and Markov chains
 3. Lamperti's problem
 4. Manydimensional random walks
 5. Heavy tails
 6. Further applications
 7. Markov chains in continuous time Glossary of named assumptions Bibliography Index.
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(source: Nielsen Book Data) 9781107026698 20170213
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QA274.73 .M46 2017  Unknown 
 Shmerkin, Pablo, author.
 Providence, RI : American Mathematical Society, [2018]
 Description
 Book — v, 102 pages : illustrations ; 26 cm.
 Summary

 IntroductionNotationThe settingHolder continuity of intersectionsClasses of spatially independent martingalesA geometric criterion for Holder continuityAffine intersections and projectionsFractal boundaries and intersections with algebraic curvesIntersections with selfsimilar sets and measuresDimension of projections: applications of Theorem 4.4Upper bounds on dimensions of intersectionsLower bounds for the dimension of intersections, and dimension conservationProducts and convolutions of spatially independent martingalesApplications to Fourier decay and restrictionBibliography.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9781470426880 20180306
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Shelved by Series title NO.1195  Unknown 
 Baldi, Paolo, 1948 author.
 Cham, Switzerland : Springer, [2017]
 Description
 Book — xiv, 627 pages : illustrations (some color) ; 24 cm.
 Summary

 1 Elements of probability.
 2 Stochastic processes.
 3 Brownian motion.
 4 Conditional probability.
 5 Martingales.
 6 Markov Processes.
 7 The stochastic integral.
 8 Stochastic calculus.
 9 Stochastic Differential Equations.
 10 PDE problems and diffusions.
 11 Simulation.
 12 Back to stochastic calculus.
 13 An application: finance. Solutions of the exercises. References. Index.
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(source: Nielsen Book Data) 9783319622255 20180423
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QA274.2 .B35 2017  Unknown 
14. Introduction to stochastic processes with R [2016]
 Dobrow, Robert P., author.
 Hoboken, New Jersey : John Wiley & Sons, Inc., [2016]
 Description
 Book — xix, 479 pages : illustrations ; 25 cm
 Summary

 Preface xi
 Acknowledgments xv
 List of Symbols and Notation xvii
 About the Companion Website xxi
 1 Introduction and Review
 1
 1.1 Deterministic and Stochastic Models
 1
 1.2 What is a Stochastic Process?
 5
 1.3 Monte Carlo Simulation
 9
 1.4 Conditional Probability
 10
 1.5 Conditional Expectation
 18
 Exercises
 34
 2 Markov Chains: First Steps
 40
 2.1 Introduction
 40
 2.2 Markov Chain Cornucopia
 42
 2.3 Basic Computations
 52
 2.4 LongTerm Behavior the Numerical Evidence
 59
 2.5 Simulation
 65
 2.6 Mathematical Inductionâ
 68
 Exercises
 70
 3 Markov Chains for the Long Term
 76
 3.1 Limiting Distribution
 76
 3.2 Stationary Distribution
 80
 3.3 Can you Find the Way to State a?
 94
 3.4 Irreducible Markov Chains
 103
 3.5 Periodicity
 106
 3.6 Ergodic Markov Chains
 109
 3.7 Time Reversibility
 114
 3.8 Absorbing Chains
 119
 3.9 Regeneration and the Strong Markov Propertyâ
 133
 3.10 Proofs of Limit Theoremsâ
 135
 Exercises
 144
 4 Branching Processes
 158
 4.1 Introduction
 158
 4.2 Mean Generation Size
 160
 4.3 Probability Generating Functions
 164
 4.4 Extinction is Forever
 168
 Exercises
 175
 5 Markov Chain Monte Carlo
 181
 5.1 Introduction
 181
 5.2 Metropolis Hastings Algorithm
 187
 5.3 Gibbs Sampler
 197
 5.4 Perfect Samplingâ
 205
 5.5 Rate of Convergence: the Eigenvalue Connectionâ
 210
 5.6 Card Shuffling and Total Variation Distanceâ
 212
 Exercises
 219
 6 Poisson Process
 223
 6.1 Introduction
 223
 6.2 Arrival, Interarrival Times
 227
 6.3 Infinitesimal Probabilities
 234
 6.4 Thinning, Superposition
 238
 6.5 Uniform Distribution
 243
 6.6 Spatial Poisson Process
 249
 6.7 Nonhomogeneous Poisson Process
 253
 6.8 Parting Paradox
 255
 Exercises
 258
 7 ContinuousTime Markov Chains
 265
 7.1 Introduction
 265
 7.2 Alarm Clocks and Transition Rates
 270
 7.3 Infinitesimal Generator
 273
 7.4 LongTerm Behavior
 283
 7.5 Time Reversibility
 294
 7.6 Queueing Theory
 301
 7.7 Poisson Subordination
 306
 Exercises
 313
 8 Brownian Motion
 320
 8.1 Introduction
 320
 8.2 Brownian Motion and Random Walk
 326
 8.3 Gaussian Process
 330
 8.4 Transformations and Properties
 334
 8.5 Variations and Applications
 345
 8.6 Martingales
 356
 Exercises
 366
 9 A Gentle Introduction to Stochastic Calculusâ
 372
 9.1 Introduction
 372
 9.2 Ito Integral
 378
 9.3 Stochastic Differential Equations
 385
 Exercises
 397
 A Getting Started with R
 400
 B Probability Review
 421
 B.1 Discrete Random Variables
 422
 B.2 Joint Distribution
 424
 B.3 Continuous Random Variables
 426
 B.4 Common Probability Distributions
 428
 B.5 Limit Theorems
 439
 B.6 MomentGenerating Functions
 440
 C Summary of Common Probability Distributions
 443
 D Matrix Algebra Review
 445
 D.1 Basic Operations
 445
 D.2 Linear System
 447
 D.3 Matrix Multiplication
 448
 D.4 Diagonal, Identity Matrix, Polynomials
 448
 D.5 Transpose
 449
 D.6 Invertibility
 449
 D.7 Block Matrices
 449
 D.8 Linear Independence and Span
 450
 D.9 Basis
 451
 D.10 Vector Length
 451
 D.11 Orthogonality
 452
 D.12 Eigenvalue, Eigenvector
 452
 D.13 Diagonalization
 453
 Answers to Selected OddNumbered Exercises
 455
 References
 470
 Index 475.
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(source: Nielsen Book Data) 9781118740651 20180611
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QC20.7 .S8 D63 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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(source: Nielsen Book Data) 9781107134607 20160619
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QA274.7 .K75 2016  Unknown 
16. Probability and random processes [2016]
 Krishnan, Venkatarama, 1929 author.
 Second edition.  Hoboken, New Jersey : John Wiley & Sons, Inc., [2016]
 Description
 Book — xv, 506 pages : illustrations ; 29 cm
 Online
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QA273 .K74 2016  Unknown 
17. Recurrent event modeling based on the Yule process : application to water network asset management [2016]
 Le Gat, Yves.
 London : ISTE Ltd ; Hoboken, NJ : John Wiley & Sons, Inc., 2016.
 Description
 Book — viii, 128 p. : ill. ; 24 cm.
 Summary

 Preface ix
 Chapter 1. Introduction
 1
 1.1. Notation
 2
 1.2. General theoretical framework
 4
 1.2.1. The concept of a counting process
 4
 1.2.2. The intensity function of a counting process
 5
 1.3. The nonhomogeneous Poisson process
 6
 1.4. The Eisenbeis model
 7
 1.5. Other approaches for water pipe failure modeling
 8
 1.6. Why mobilize the Yule process?
 9
 1.7. Structure of the book
 10
 Chapter 2. Preliminaries
 13
 2.1. The Yule process and the negative binomial distribution
 13
 2.2. Gammamixture of NHPP
 17
 2.3. The negative binomial power series
 19
 2.4. The negative multinomial distribution
 19
 2.5. The negative multinomial power series
 22
 Chapter 3. Nonhomogeneous Birth Process
 23
 3.1. NHBP intensity
 24
 3.2. Conditional distribution of the counting process
 24
 Chapter 4. Linear Extension of the Yule Process
 33
 4.1. LEYP intensity
 33
 4.2. Conditional distribution of the LEYP
 34
 4.2.1. Distribution of N(b) N(a)
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(source: Nielsen Book Data) 9781848218918 20180611
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QC20.7 .S8 L4 2016  Unknown 
18. Stochastic porous media equations [2016]
 Barbu, Viorel, 1941 author.
 [Cham] Switzerland : Springer, [2016]
 Description
 Book — ix, 202 pages ; 24 cm.
 Summary

 Foreword. Preface. Introduction. Equations with Lipschitz nonlinearities. Equations with maximal monotone nonlinearities. Variational approach to stochastic porous media equations. L1based approach to existence theory for stochastic porous media equations. The stochastic porous media equations in Rd. Transition semigroups and ergodicity of invariant measures. Kolmogorov equations. A Two analytical inequalities. Bibliography. Glossary. Translator's note. Index.
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(source: Nielsen Book Data) 9783319410685 20161219
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Serials  
Shelved by Series title V.2163  Unknown 
 Jagna International Workshop (7th : 2014 : Jagna, Bohol, Philippines)
 Hackensack, New Jersey : World Scientific, [2015]
 Description
 Book — 1 volume (various pagings) : illustrations ; 26 cm
 Summary

 Anomalous Diffusion Processes Fractional Path Integrals Fractional Brownian Motion and Polymers Probing Cell Mechanics with Optical Tweezers Diffusion of AlphaHelical Proteins Space Fractional Schrodinger Equation Multifractional Processes Path Summation with Memory Grey Brownian Motion Fractional Dynamics of Carrier Transport in Organic Semiconductors Photostimulation of Neurons Modeling Urban Dynamics.
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(source: Nielsen Book Data) 9789814618342 20160618
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QC20.7 .S8 J34 2014  Unknown 
20. Basic stochastic processes [2015]
 Devolder, Pierre.
 London : ISTE ; Hoboken, NJ : Wiley, c2015.
 Description
 Book — xii, 310 p. : ill. ; 24 cm.
 Summary

 INTRODUCTION xi
 CHAPTER 1. BASIC PROBABILISTIC TOOLS FOR STOCHASTIC MODELING
 1
 1.1. Probability space and random variables
 1
 1.2. Expectation and independence
 4
 1.3. Main distribution probabilities
 7
 1.3.1. Binomial distribution
 7
 1.3.2. Negative exponential distribution
 8
 1.3.3. Normal (or Laplace Gauss) distribution
 8
 1.3.4. Poisson distribution
 11
 1.3.5. Lognormal distribution
 11
 1.3.6. Gamma distribution
 12
 1.3.7. Pareto distribution
 13
 1.3.8. Uniform distribution
 16
 1.3.9. Gumbel distribution
 16
 1.3.10. Weibull distribution
 16
 1.3.11. Multidimensional normal distribution
 17
 1.3.12. Extreme value distribution
 19
 1.4. The normal power (NP) approximation
 28
 1.5. Conditioning
 31
 1.6. Stochastic processes
 39
 1.7. Martingales
 43
 CHAPTER 2. HOMOGENEOUS AND NONHOMOGENEOUS RENEWAL MODELS
 47
 2.1. Introduction
 47
 2.2. Continuous time nonhomogeneous convolutions
 49
 2.2.1. Nonhomogeneous convolution product
 49
 2.3. Homogeneous and nonhomogeneous renewal processes
 53
 2.4. Counting processes and renewal functions
 56
 2.5. Asymptotical results in the homogeneous case
 61
 2.6. Recurrence times in the homogeneous case
 63
 2.7. Particular case: the Poisson process
 66
 2.7.1. Homogeneous case
 66
 2.7.2. Nonhomogeneous case
 68
 2.8. Homogeneous alternating renewal processes
 69
 2.9. Solution of nonhomogeneous discrete timevevolution equation
 71
 2.9.1. General method
 71
 2.9.2. Some particular formulas
 73
 2.9.3. Relations between discrete time and continuous time renewal equations
 74
 CHAPTER 3. MARKOV CHAINS
 77
 3.1. Definitions
 77
 3.2. Homogeneous case
 78
 3.2.1. Basic definitions
 78
 3.2.2. Markov chain state classification
 81
 3.2.3. Computation of absorption probabilities
 87
 3.2.4. Asymptotic behavior
 88
 3.2.5. Example: a management problem in an insurance company
 93
 3.3. Nonhomogeneous Markov chains
 95
 3.3.1. Definitions
 95
 3.3.2. Asymptotical results
 98
 3.4. Markov reward processes
 99
 3.4.1. Classification and notation
 99
 3.5. Discrete time Markov reward processes (DTMRWPs)
 102
 3.5.1. Undiscounted case
 102
 3.5.2. Discounted case
 105
 3.6. General algorithms for the DTMRWP
 111
 3.6.1. Homogeneous MRWP
 112
 3.6.2. Nonhomogeneous MRWP
 112
 CHAPTER 4. HOMOGENEOUS AND NONHOMOGENEOUS SEMIMARKOV MODELS
 113
 4.1. Continuous time semiMarkov processes
 113
 4.2. The embedded Markov chain
 117
 4.3. The counting processes and the associated semiMarkov process
 118
 4.4. Initial backward recurrence times
 120
 4.5. Particular cases of MRP
 122
 4.5.1. Renewal processes and Markov chains
 122
 4.5.2. MRP of zeroorder (PYKE (1962))
 122
 4.5.3. Continuous Markov processes
 124
 4.6. Examples
 124
 4.7. Discrete time homogeneous and nonhomogeneous semiMarkov processes
 127
 4.8. SemiMarkov backward processes in discrete time
 129
 4.8.1. Definition in the homogeneous case
 129
 4.8.2. SemiMarkov backward processes in discrete time for the nonhomogeneous case
 130
 4.8.3. DTSMP numerical solutions
 133
 4.9. Discrete time reward processes
 137
 4.9.1. Undiscounted SMRWP
 137
 4.9.2. Discounted SMRWP
 141
 4.9.3. General algorithms for DTSMRWP
 144
 4.10. Markov renewal functions in the homogeneous case
 146
 4.10.1. Entrance times
 146
 4.10.2. The Markov renewal equation
 150
 4.10.3. Asymptotic behavior of an MRP
 151
 4.10.4. Asymptotic behavior of SMP
 153
 4.11. Markov renewal equations for the nonhomogeneous case
 158
 4.11.1. Entrance time
 158
 4.11.2. The Markov renewal equation
 162
 CHAPTER 5. STOCHASTIC CALCULUS
 165
 5.1. Brownian motion
 165
 5.2. General definition of the stochastic integral
 167
 5.2.1. Problem of stochastic integration
 167
 5.2.2. Stochastic integration of simple predictable processes and semimartingales
 168
 5.2.3. General definition of the stochastic integral
 170
 5.3. Ito s formula
 177
 5.3.1. Quadratic variation of a semimartingale
 177
 5.3.2. Ito s formula
 179
 5.4. Stochastic integral with standard Brownian motion as an integrator process
 180
 5.4.1. Case of simple predictable processes
 181
 5.4.2. Extension to general integrator processes
 183
 5.5. Stochastic differentiation
 184
 5.5.1. Stochastic differential
 184
 5.5.2. Particular cases
 184
 5.5.3. Other forms of Ito s formula
 185
 5.6. Stochastic differential equations
 191
 5.6.1. Existence and unicity general theorem
 191
 5.6.2. Solution of stochastic differential equations
 195
 5.6.3. Diffusion processes
 199
 5.7. Multidimensional diffusion processes
 202
 5.7.1. Definition of multidimensional Ito and diffusion processes
 203
 5.7.2. Properties of multidimensional diffusion processes
 203
 5.7.3. Kolmogorov equations
 205
 5.7.4. The Stroock Varadhan martingale characterization of diffusion processes
 208
 5.8. Relation between the resolution of PDE and SDE problems. The Feynman Kac formula
 209
 5.8.1. Terminal payoff
 209
 5.8.2. Discounted payoff function
 210
 5.8.3. Discounted payoff function and payoff rate
 210
 5.9. Application to option theory
 213
 5.9.1. Options
 213
 5.9.2. Black and Scholes model
 216
 5.9.3. The Black and Scholes partial differential equation (BSPDE) and the BS formula
 216
 5.9.4. Girsanov theorem
 219
 5.9.5. The riskneutral measure and the martingale property
 221
 5.9.6. The riskneutral measure and the evaluation of derivative products
 224
 CHAPTER 6. LEVY PROCESSES
 227
 6.1. Notion of characteristic functions
 227
 6.2. Levy processes
 228
 6.3. Levy Khintchine formula
 230
 6.4. Subordinators
 234
 6.5. Poisson measure for jumps
 234
 6.5.1. The Poisson random measure
 234
 6.5.2. The compensated Poisson process
 235
 6.5.3. Jump measure of a Levy process
 236
 6.5.4. The Ito Levy decomposition
 236
 6.6. Markov and martingale properties of Levy processes
 237
 6.6.1. Markov property
 237
 6.6.2. Martingale properties
 239
 6.6.3. Ito formula
 240
 6.7. Examples of Levy processes
 240
 6.7.1. The lognormal process: Black and Scholes process
 240
 6.7.2. The Poisson process
 241
 6.7.3. Compensated Poisson process
 242
 6.7.4. The compound Poisson process
 242
 6.8. Variance gamma (VG) process
 244
 6.8.1. The gamma distribution
 244
 6.8.2. The VG distribution
 245
 6.8.3. The VG process
 246
 6.8.4. The Esscher transformation
 247
 6.8.5. The Carr Madan formula for the European call
 249
 6.9. Hyperbolic Levy processes
 250
 6.10. The Esscher transformation
 252
 6.10.1. Definition
 252
 6.10.2. Option theory with hyperbolic Levy processes
 253
 6.10.3. Value of the European option call
 255
 6.11. The Brownian Poisson model with jumps
 256
 6.11.1. Mixed arithmetic Brownian Poisson and geometric Brownian Poisson processes
 256
 6.11.2. Merton model with jumps
 258
 6.11.3. Stochastic differential equation (SDE) for mixed arithmetic Brownian Poisson and geometric Brownian Poisson processes
 261
 6.11.4. Value of a European call for the lognormal Merton model
 264
 6.12. Complete and incomplete markets
 264
 6.13. Conclusion
 265
 CHAPTER 7. ACTUARIAL EVALUATION, VAR AND STOCHASTIC INTEREST RATE MODELS
 267
 7.1. VaR technique
 267
 7.2. Conditional VaR value
 271
 7.3. Solvency II
 276
 7.3.1. The SCR indicator
 276
 7.3.2. Calculation of MCR
 278
 7.3.3. ORSA approach
 279
 7.4. Fair value
 280
 7.4.1. Definition
 280
 7.4.2. Market value of financial flows
 281
 7.4.3. Yield curve
 281
 7.4.4. Yield to maturity for a financial investment and a bond
 283
 7.5. Dynamic stochastic time continuous time model for instantaneous interest rate
 284
 7.5.1. Instantaneous deterministic interest rate
 284
 7.5.2. Yield curve associated with a deterministic instantaneous interest rate
 285
 7.5.3. Dynamic stochastic continuous time model for instantaneous interest rate
 286
 7.5.4. The OUV stochastic model
 287
 7.5.5. The CIR model
 289
 7.6. Zerocoupon pricing under the assumption of no arbitrage
 292
 7.6.1. Stochastic dynamics of zerocoupons
 292
 7.6.2. The CIR process as rate dynamic
 295
 7.7. Market evaluation of financial flows
 298
 BIBLIOGRAPHY
 301
 INDEX 309.
 (source: Nielsen Book Data)
(source: Nielsen Book Data) 9781848218826 20180611
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA274 .D475 2015  Unknown 