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1. A Celebration of applied probability [1988]
 Sheffield, England : Applied Probability Trust, c1988.
 Description
 Book — x, 387 p. : ill. ; 25 cm.
 Online
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510.5 .J868 V.25A  Available 
 [Sheffield, Eng.] Applied Probability Trust.
 Description
 Journal/Periodical — no. ill. 25 cm.
 Online
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QA276 .A1 A32 NO.14 20072009  Available 
QA276 .A1 A32 NO.13 20042006  Available 
QA276 .A1 A32 NO.12 20012003  Available 
QA276 .A1 A32 NO.11 19982000  Available 
QA276 .A1 A32 NO.10 19951997  Available 
QA276 .A1 A32 NO.9 19921994  Available 
QA276 .A1 A32 NO.8 1992  Available 
QA276 .A1 A32 NO.7 1989  Available 
QA276 .A1 A32 NO.6 1986  Available 
QA276 .A1 A32 NO.5 1983  Available 
QA276 .A1 A32 NO.4 1980  Available 
QA276 .A1 A32 NO.3 1977  Available 
QA276 .A1 A32 NO.2 1974  Available 
QA276 .A1 A32 NO.1 1971  Available 
 Applied probability complete author and subject index (Online)
 [Sheffield, Eng. : Applied Probability Trust]
 Description
 Journal/Periodical
 Brémaud, Pierre.
 Cham : Springer, 2020.
 Description
 Book — 1 online resource (717 p.). Digital: text file; PDF.
 Summary

 Introduction.Warming Up. Integration Theory for Probability. Probability and Expectation. Convergence of random sequences. Markov Chains. Martingale Sequences. Ergodic Sequences. Generalities on Stochastic Processes. Poisson Processes. ContinuousTime Markov Chains. Renewal Theory in Continuous Time. Brownian Motion. Widesense Stationary Stochastic Processes. An Introduction to Ito's Calculus. Appenndix: Number Theory and Linear Algebra. Analysis. Hilbert Spaces. ZTransforms. Proof of Paul Levy's Criterion. Direct Riemann Integrability. Bibliography. Index. .
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 Intro
 Contents
 Introduction
 PART ONE: Probability theory
 PART TWO: Standard stochastic processes
 PART THREE: Advanced topics
 Practical issues
 Acknowledgements
 I: PROBABILITY THEORY
 Chapter 1 Warming Up
 1.1 Sample Space, Events and Probability
 1.1.1 Events
 The Language of Probabilists
 The σfield of Events
 1.1.2 Probability of Events
 Basic Formulas
 Negligible Sets
 1.2 Independence and Conditioning
 1.2.1 Independent Events
 1.2.2 Bayes' Calculus
 1.2.3 Conditional Independence
 1.3 Discrete Random Variables
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 Cham, Switzerland : Birkhäuser, [2019]
 Description
 Book — x, 455 pages ; 24 cm
 Summary

 Jorgen HoffmannJorgensen (19422017). Moment estimation implied by the BobkovLedoux inequality. Polar Isoperimetry. I: The case of the Plane. Iterated Jackknives and TwoSided Variance Inequalities. A Probabilistic Characterization of Negative Definite Functions. Higher Order Concentration in presence of Poincaretype inequalities. Rearrangement and PrekopaLeindler Type Inequalities. Generalized Semimodularity: Order Statistics. Geometry of np Balls: Classical Results and Recent Developments. Remarks on Superconcentration and Gamma calculus. Application to Spin Glasses. Asymptotic behavior of Renyi entropy in the Central Limit Theorem. UniforminBandwidth Functional Limit Laws for Multivariate Empirical Processes. Universality of Limiting Spectral Distribution Under Projective Criteria. Exchangeable Pairs on Wiener Chaos. Permanental Processes with Kernels That Are Not Equivalent to a Symmetric Matrix. Pointwise Properties of Martingales with Values in Banach Function Spaces. Concentration Inequalities for Randomly Permuted Sums. Uncertainty Quantification for Matrix Compressed Sensing and Quantum Tomography Problems. Uniform in Bandwidth Estimation of the Gradient Lines of a Density.
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QA273 .H6435 2019  Unknown 
 Cham : Springer, 2019.
 Description
 Book — 1 online resource (viii, 562 p.) : ill. (some col.).
 Summary

  Part I In memoriam Jacques Azema.  Un temoignage.  Un dimanche de juin avec Jacques.  Mosaique de PoissonVoronoi sur une surface.  Sur le retournement du temps.  La martingale d'Azema.  Part II Regular Contributions.  Complementability and Maximality in Different Contexts: Ergodic Theory, Brownian and PolyAdic Filtrations.  Uniform Entropy Scalings of Filtrations.  Solving Rough Differential Equations with the Theory of Regularity Structures.  On the EulerMaruyama Scheme for Degenerate Stochastic Differential Equations with Nonsticky Condition.  On a Construction of Strong Solutions for Stochastic Differential Equations with NonLipschitz Coefficients: A Priori Estimates Approach.  Heat Kernel Coupled with Geometric Flow and Ricci Flow.  Scaled Penalization of Brownian Motion with Drift and the Brownian Ascent.  Interlacing Diffusions.  Brownian Sheet Indexed by RN: Local Time and Bubbles.  Mod Convergence, II: Estimates on the Speed of Convergence.  Random Flows Defined by Markov Loops.  Brownian Winding Fields.  Recurrence and Transience of ContinuousTime Open Quantum Walks.  Explicit Speed of Convergence of the Stochastic Billiard in a Convex Set.
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7. Foundations of the theory of probability [1956]
 Grundbegriffe der Wahrscheinlichkeitsrechnung. English
 Kolmogorov, A. N. (Andreĭ Nikolaevich), 19031987 author.
 Second English edition, Dover edition.  Muneola, New York : Dover Publications, Inc., 2018.
 Description
 Book — 1 online resource.
 Mérő, László, author.
 New Haven, CT : Yale University Press, [2018]
 Description
 Book — xii, 275 pages ; 22 cm
 Summary

We live in a much more turbulent world than we like to think, but the science we use to analyze economic, financial, and statistical events mostly disregards the world's essentially chaotic nature. We need to get used to the idea that wildly improbable events are actually part of the natural order. The renowned Hungarian mathematician and psychologist Lï¿½szlï¿½ Mï¿½ro explains how the wild and mild worlds (which he names Wildovia and Mildovia) coexist, and that different laws apply to each. Even if we live in an ultimately wild universe, he argues, we're better off pretending that it obeys Mildovian laws. Doing so may amount to a selffulfilling prophecy and create an island of predictability in a very rough sea. Perched on the ragged border between economics and complexity theory, Mï¿½ro proposes to extend the reach of science to subjects previously considered outside its grasp: the unpredictable, unrepeatable, highly improbable events we commonly call "miracles.".
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QA273 .M47 2018  Unknown 
9. Séminaire de Probabilités XLIX [2018]
 Cham, Switzerland : Springer, [2018]
 Description
 Book — viii, 542 pages : illustrations (some color) ; 24 cm.
 Summary

  OrnsteinUhlenbeck Pinball and the Poincare Inequality in a Punctured Domain.  A Probabilistic Look at Conservative GrowthFragmentation Equations.  Iterated Proportional Fitting Procedure and Infinite Products of Stochastic Matrices.  Limiting Eigenvectors of Outliers for Spiked InformationPlusNoise Type Matrices.  Criteria for Exponential Convergence to QuasiStationary Distributions and Applications to MultiDimensional Diffusions.  BismutElworthyLi Formulae for Bessel Processes.  Large Deviations for Infectious Diseases Models.  The Girsanov Theorem Without (So Much) Stochastic Analysis.  On Drifting Brownian Motion Made Periodic.  On the Markovian Similarity.  Sharp Rate for the Dual Quantization Problem.  Cramer's Theorem in Banach Spaces Revisited.  On Martingale Chaoses.  Explicit Laws for the Records of the Perturbed Random Walk on Z.  A Potential Theoretic Approach to Tanaka Formula for Asymmetric Levy Processes.
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Shelved by Series title V.2215  Unknown 
10. Theory of Probability [1998]
 Gnedenko, Boris V., author.
 Sixth edition  Boca Raton, FL : Routledge, [2018]
 Description
 Book — 1 online resource (520 pages)
 Summary

 1. Random Events and Their Probabilities
 2. Sequences in Independent Trials
 3. Markov Chains
 4. Random Valuables and Distribution Functions
 5. Numberical Characteristics of Random Variables
 6. The Law of Large Numbers
 7. Characteristic Functions
 8. The Classical Limit Theorem
 9. The Theory of Infinitely Divisible Distributions
 10. The Theory of Stochastic Processes
 11. The Elements of Statistics Appendix.
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 Carlton, Matthew A. author.
 Second edition.  Cham, Switzerland : Springer, [2017]
 Description
 Book — xxv, 610 pages ; 26 cm.
 Summary

 Probability. Discrete Random Variables and Probability Distributions. Continuous Random Variables and Probability Distributions. Joint probability distributions and their applications. The Basics of Statistical Inference. Markov chains. Random processes. Introduction to signal processing.
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QA273 .C258 2017  Unknown 
12. A basic course in probability theory [2016]
 Bhattacharya, R. N. (Rabindra Nath), 1937 author.
 Second edition.  Cham, Switzerland : Springer, 2016.
 Description
 Book — 1 online resource (xii, 265 pages). Digital: text file; PDF.
 Summary

 Preface to Second Edition. Preface to First Edition. I. Random Maps, Distribution, and Mathematical Expectation. II. Independence, Conditional Expectation. III. Martingales and Stopping Times. IV. Classical Central Limit Theorems. V. Classical ZeroOne Laws, Laws of Large Numbers and Large Deviations. VI. Fourier Series, Fourier Transform, and Characteristic Functions. VII. Weak Convergence of Probability Measures on Metric Spaces. VIII. Random Series of Independent Summands. IX. Kolmogorov's Extension Theorem and Brownian Motion. X. Brownian Motion: The LIL and Some FineScale Properties. XI. Strong Markov Property, Skorokhod Embedding and Donsker's Invariance Principle. XII. A Historical Note on Brownian Motion. XIII. Some Elements of the Theory of Markov Processes and their Convergence to Equilibrium. A. Measure and Integration. B. Topology and Function Spaces. C. Hilbert Spaces and Applications in Measure Theory. References. Symbol Index. Subject Index.
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13. Probability [2016  2019]
 Veroi͡atnostʹ. English
 Shiri͡aev, A. N. (Alʹbert Nikolaevich) author.
 Third edition, expanded and updated.  New York ; Heidelberg : Springer, [2016][2019]
 Description
 Book — 2 volumes : illustrations ; 25 cm.
 Summary

 Vol. 1
 Preface to the third English edition
 Preface to the fourth Russian edition
 Preface to the third Russian edition
 Preface to the second edition
 Preface to the first edition
 Introduction
 Elementary probability theory
 Probabilistic model of an experiment with a finite
 Number of outcomes
 Some classical models and distributions
 Conditional probability : independence
 Random variables and their properties
 The bernoulli scheme : ithe law of large numbers
 The bernoulli scheme : iilimit theorems (Local, de MoivreLaplace, Poisson)
 Estimating the probability of success in the bernoulli scheme
 Conditional probabilities and expectations with respect to decompositions
 Random walk : iprobabilities of ruin and mean
 Duration in coin tossing
 Random walk : iireflection principlearcsine law
 Martingales : some applications to the random walk
 Markov chains : ergodic theorem, strong markov property
 Generating functions
 Inclusionexclusion principle
 Mathematical foundations of probability theory
 Kolmogorov's Axioms
 Algebras and aalgebras : measurable spaces
 Methods of introducing probability measures on measurable spaces
 Random variables : I
 Random elements
 Lebesgue integral : expectation
 Conditional probabilities and conditional expectations with respect to a a algebra
 Random variables : II
 Construction of a process with given finitedimensional distributions
 Various kinds of convergence of sequences of random variables
 The hubert space of random variables with finite second moment
 Characteristic functions
 Gaussian systems
 Convergence of probability measures : central limit theorem
 Weak convergence of probability measures and distributions
 Relative compactness and tightness of families of probability distributions
 Proof of limit theorems by the method of characteristic functions
 Central limit theorem : I
 central limit theorem for sums of independent random variables : II
 Infinitely divisible and stable distributions
 Metrizability of weak convergence
 On the connection of weak convergence of measures
 The distance in variation between probability measures
 Contiguity of probability measures
 Rate of convergence in the central limit theorem
 Rate of convergence in poisson's theorem
 Fundamental theorems of mathematical statistics
 Historical and bibliographical notes
 References
 Keyword index
 Symbol index.
 Vol. 2
 Preface to the Third English Edition
 Preface to the Fourth Russian Edition
 Sequences and Sums of Independent Random Variables
 ZeroOne Laws
 Convergence of Series
 Strong Law of Large Numbers
 Law of the Iterated Logarithm
 Probabilities of Large Deviations
 Stationary (Strict Sense) Random Sequences and Ergodic Theory
 Stationary (Strict Sense) Random Sequences : MeasurePreserving Transformations
 Ergodicity and Mixing
 Ergodic Theorems
 Stationary (Wide Sense) Random Sequences : L2Theory
 Spectral Representation of the Covariance Function
 Orthogonal Stochastic Measures and Stochastic Integrals
 Spectral Representation of Stationary (Wide Sense) Sequences
 Statistical Estimation of Covariance Function and Spectral Density
 Wold's Expansion
 Extrapolation, Interpolation, and Filtering
 The KalmanBucy Filter and Its Generalizations
 Martingales
 Definitions of Martingales and Related Concepts
 Preservation of Martingale Property Under a Random Time Change
 Fundamental Inequalities
 General Theorems on Convergence of Submartingales and Martingales
 Sets of Convergence of Submartingales and Martingales
 Absolute Continuity and Singularity of Probability Distributions on a Measurable Space with Filtration
 Asymptotics of the Probability of the Outcome of a Random Walk with Curvilinear Boundary
 Central Limit Theorem for Sums of Dependent Random Variables
 Discrete Version of Itô's Formula
 Application of Martingale Methods to Calculation of Probability of Ruin in Insurance
 Fundamental Theorems of Stochastic Financial Mathematics : The Martingale Characterization of the Absence of Arbitrage
 Hedging in ArbitrageFree Models
 Optimal Stopping Problems : Martingale Approach
 Markov Chains
 Definitions and Basic Properties
 Generalized Markov and Strong Markov Properties
 Limiting, Ergodic, and Stationary Probability Distributions for Markov Chains
 Classification of States of Markov Chains in Terms of Algebraic Properties of Matrices of Transition Probabilities
 Classification of States of Markov Chains in Terms of Asymptotic Properties of Transition Probabilities
 Limiting, Stationary, and Ergodic Distributions for Countable Markov Chains
 Limiting, Stationary, and Ergodic Distributions for Finite Markov Chains
 Simple Random Walk as a Markov Chain
 Optimal Stopping Problems for Markov Chains
 Historical Review
 Historical and Bibliographical Notes (Chaps. 48)
 References
 Index.
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QA273 .S54413 2016 V.1  Unknown 
QA273 .S54413 2016 V.2  Unknown 
14. Probability. 1 [2016]
 Shiri͡aev, Alʹbert Nikolaevich, author.
 Third edition / translated by Stephen S. Wilson.  New York : Springer, 2016.
 Description
 Book — 1 online resource (xvii, 486 pages).
 Summary

 Introduction. Elementary Probability Theory. Mathematical Foundations of Probability Theory. Convergence of Probability Measures. Central Limit Theorem.
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15. Séminaire de probabilités XLVIII / Catherine DonatiMartin, Antoine Lejay, Alain Rouault, editors [2016]
 Séminaire de probabilités (48th)
 1st ed.  [Cham], Switzerland : Springer, [2016]
 Description
 Book — vii, 503 pages : illustrations ; 24 cm.
 Summary

 Mathias Beiglböck, Martin Huesmann and Florian Stebegg: Root to Kellerer
 Nicolas Juillet: Peacocks Parametrised by a Partially Ordered Set
 Convex order for pathdependent derivatives: a dynamic programming approach
 Dai Taguchi: Stability problem for onedimensional stochastic differential equations with discontinuous drift
 Alexis Devulder: The Maximum of the Local Time of a Diffusion Process in a Drifted Brownian Potential
 Mátyás Barczy and Peter Kern: A link between Bougerol's identity and a formula due to DonatiMartin, Matsumoto and Yor
 Ismal Bailleul: Large deviation principle for bridges of subRiemannian diffus ion processes
 Jürgen Angst and Camille Tardif: Dévissage of a Poisson boundary under equivariance and regularity conditions
 Nicolas Privault: Weitzenböck and ClarkOcone decompositions for differential forms on the space of normal martingales
 Anita Behme, Alexander Lindner and Makoto Maejima: On the range of exponential functionals of Lévy processes
 Cédric Lecouvey and Kilian Raschel: tMartin boundary of killed random walks in the quadrant
 Christophe Profeta and Thomas Simon: On the harmonic measure of stable processes
 Oleskiy Khorunzhiy: On High Moments of Strongly Diluted Large Wigner Random Matrices
 Songzi Li: Dyson processes on the octonion algebra
 Franck Maunoury: Necessary and sufficient conditions for the existence of adeterminantal processes
 Stéphane Laurent: Filtrations of the erasedword processes
 Anna Aksamit and Libo Li: Projections, pseudostopping times and the immersion property
 David Applebaum: Stationary Random Fields on the Unitary Dual of a Compact Group
 Wendelin Werner: On the spatial Markov property of soups of unoriented and oriented loops.
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Shelved by Series title V.2168  Unknown 
 BenNaim, Arieh, 1934 author.
 Hackensack, New Jersey : World Scientific, [2015]
 Description
 Book — xix, 318 pages : illustrations ; 24 cm
 Summary

 What is the Probability? How Do We Calculate Probabilities? The Axiomatic Approach to Probability Independence and Dependence Between Events Bayes' Theorem and Its Applications Average, Variance and Random Variable Probability Distributions Shannon's Measure of Information.
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QA273 .B445 2015  Unknown 
17. Vvedenie v teorii͡u veroi͡atnosteĭ [2015]
 Введение в теорию вероятностей
 Kolmogorov, A. N. (Andreĭ Nikolaevich), 19031987 author.
 Колмогоров, А. Н. (Андрей Николаевич), 19031987, author.
 Izdanie tretʹe, ispravlennoe. Издание третье, исправленное.  Moskva : Izdatelʹstvo MT͡SNMO, 2015. Москва : Издательство МЦНМО, 2015.
 Description
 Book — 168 pages : illustrations ; 20 cm.
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QA273 .K618 2015  Available 
18. Handbook of probability [2014]
 Florescu, Ionuţ, 1973
 Hoboken, New Jersey : John Wiley & Sons, Inc., [2014]
 Description
 Book — xx, 449 pages : illustrations ; 25 cm.
 Summary

 List of Figures xv Preface xvii Introduction xix
 1 Probability Space 1 1.1 Introduction/Purpose of the
 Chapter 1 1.2 Vignette/Historical Notes 2 1.3 Notations and Definitions 2 1.4 Theory and Applications 4 1.4.1 Algebras 4 1.4.2 Sigma Algebras 5 1.4.3 Measurable Spaces 7 1.4.4 Examples 7 1.4.5 The Borel Algebra 9 1.5 Summary 12 Exercises 12
 2 Probability Measure 15 2.1 Introduction/Purpose of the
 Chapter 15 2.2 Vignette/Historical Notes 16 2.3 Theory and Applications 17 2.3.1 Definition and Basic Properties 17 2.3.2 Uniqueness of Probability Measures 22 2.3.3 Monotone Class 24 2.3.4 Examples 26 2.3.5 Monotone Convergence Properties of Probability 28 2.3.6 Conditional Probability 31 2.3.7 Independence of Events and Fields 39 2.3.8 Borel Cantelli Lemmas 46 2.3.9 Fatou s Lemmas 48 2.3.10 Kolmogorov s Zero One Law 49 2.4 Lebesgue Measure on the Unit Interval (01] 50 Exercises 52
 3 Random Variables: Generalities 63 3.1 Introduction/Purpose of the
 Chapter 63 3.2 Vignette/Historical Notes 63 3.3 Theory and Applications 64 3.3.1 Definition 64 3.3.2 The Distribution of a Random Variable 65 3.3.3 The Cumulative Distribution Function of a Random Variable 67 3.3.4 Independence of Random Variables 70 Exercises 71
 4 Random Variables: The Discrete Case 79 4.1 Introduction/Purpose of the
 Chapter 79 4.2 Vignette/Historical Notes 80 4.3 Theory and Applications 80 4.3.1 Definition and Basic Facts 80 4.3.2 Moments 84 4.4 Examples of Discrete Random Variables 89 4.4.1 The (Discrete) Uniform Distribution 89 4.4.2 Bernoulli Distribution 91 4.4.3 Binomial (n p) Distribution 92 4.4.4 Geometric (p) Distribution 95 4.4.5 Negative Binomial (r p) Distribution 101 4.4.6 Hypergeometric Distribution (N m n) 102 4.4.7 Poisson Distribution 104 Exercises 108
 5 Random Variables: The Continuous Case 119 5.1 Introduction/Purpose of the
 Chapter 119 5.2 Vignette/Historical Notes 119 5.3 Theory and Applications 120 5.3.1 Probability Density Function (p.d.f.) 120 5.3.2 Cumulative Distribution Function (c.d.f.) 124 5.3.3 Moments 127 5.3.4 Distribution of a Function of the Random Variable 128 5.4 Examples 130 5.4.1 Uniform Distribution on an Interval [ab] 130 5.4.2 Exponential Distribution 133 5.4.3 Normal Distribution ( 2) 136 5.4.4 Gamma Distribution 139 5.4.5 Beta Distribution 144 5.4.6 Student s t Distribution 147 5.4.7 Pareto Distribution 149 5.4.8 The LogNormal Distribution 151 5.4.9 Laplace Distribution 153 5.4.10 Double Exponential Distribution 155 Exercises 156
 6 Generating Random Variables 177 6.1 Introduction/Purpose of the
 Chapter 177 6.2 Vignette/Historical Notes 178 6.3 Theory and Applications 178 6.3.1 Generating OneDimensional Random Variables by Inverting the Cumulative Distribution Function (c.d.f.) 178 6.3.2 Generating OneDimensional Normal Random Variables 183 6.3.3 Generating Random Variables. Rejection Sampling Method 186 6.3.4 Generating from a Mixture of Distributions 193 6.3.5 Generating Random Variables. Importance Sampling 195 6.3.6 Applying Importance Sampling 198 6.3.7 Practical Consideration: Normalizing Distributions 201 6.3.8 Sampling Importance Resampling 203 6.3.9 Adaptive Importance Sampling 204 6.4 Generating Multivariate Distributions with Prescribed Covariance Structure 205 Exercises 208
 7 Random Vectors in Rn 210 7.1 Introduction/Purpose of the
 Chapter 210 7.2 Vignette/Historical Notes 210 7.3 Theory and Applications 211 7.3.1 The Basics 211 7.3.2 Marginal Distributions 212 7.3.3 Discrete Random Vectors 214 7.3.4 Multinomial Distribution 219 7.3.5 Testing Whether Counts are Coming from a Specific Multinomial Distribution 220 7.3.6 Independence 221 7.3.7 Continuous Random Vectors 223 7.3.8 Change of Variables. Obtaining Densities of Functions of Random Vectors 229 7.3.9 Distribution of Sums of Random Variables. Convolutions 231 Exercises 236
 8 Characteristic Function 255 8.1 Introduction/Purpose of the
 Chapter 255 8.2 Vignette/Historical Notes 255 8.3 Theory and Applications 256 8.3.1 Definition and Basic Properties 256 8.3.2 The Relationship Between the Characteristic Function and the Distribution 260 8.4 Calculation of the Characteristic Function for Commonly Encountered Distributions 265 8.4.1 Bernoulli and Binomial 265 8.4.2 Uniform Distribution 266 8.4.3 Normal Distribution 267 8.4.4 Poisson Distribution 267 8.4.5 Gamma Distribution 268 8.4.6 Cauchy Distribution 269 8.4.7 Laplace Distribution 270 8.4.8 Stable Distributions. L'evy Distribution 271 8.4.9 Truncated L'evy Flight Distribution 274 Exercises 275
 9 MomentGenerating Function 280 9.1 Introduction/Purpose of the
 Chapter 280 9.2 Vignette/Historical Notes 280 9.3 Theory and Applications 281 9.3.1 Generating Functions and Applications 281 9.3.2 MomentGenerating Functions. Relation with the Characteristic Functions 288 9.3.3 Relationship with the Characteristic Function 292 9.3.4 Properties of the MGF 292 Exercises 294
 10 Gaussian Random Vectors 300 10.1 Introduction/Purpose of the
 Chapter 300 10.2 Vignette/Historical Notes 301 10.3 Theory and Applications 301 10.3.1 The Basics 301 10.3.2 Equivalent Definitions of a Gaussian Vector 303 10.3.3 Uncorrelated Components and Independence 309 10.3.4 The Density of a Gaussian Vector 313 10.3.5 Cochran s Theorem 316 10.3.6 Matrix Diagonalization and Gaussian Vectors 319 Exercises 325
 11 Convergence Types. Almost Sure Convergence. LpConvergence. Convergence in Probability 338 11.1 Introduction/Purpose of the
 Chapter 338 11.2 Vignette/Historical Notes 339 11.3 Theory and Applications: Types of Convergence 339 11.3.1 Traditional Deterministic Convergence Types 339 11.3.2 Convergence of Moments of an r.v. Convergence in Lp 341 11.3.3 Almost Sure (a.s.) Convergence 342 11.3.4 Convergence in Probability 344 11.4 Relationships Between Types of Convergence 346 11.4.1 a.s. and Lp 347 11.4.2 Probability and a.s./Lp 351 11.4.3 Uniform Integrability 357 Exercises 359
 12 Limit Theorems 372 12.1 Introduction/Purpose of the
 Chapter 372 12.2 Vignette/Historical Notes 372 12.3 Theory and Applications 375 12.3.1 Weak Convergence 375 12.3.2 The Law of Large Numbers 384 12.4 Central Limit Theorem 401 Exercises 409
 13 Appendix A: Integration Theory. General Expectations 421 13.1 Integral of Measurable Functions 422 13.1.1 Integral of Simple (Elementary) Functions 422 13.1.2 Integral of Positive Measurable Functions 424 13.1.3 Integral of Measurable Functions 428 13.2 General Expectations and Moments of a Random Variable 429 13.2.1 Moments and Central Moments. Lp Space 430 13.2.2 Variance and the Correlation Coefficient 431 13.2.3 Convergence Theorems 433
 14 Appendix B: Inequalities Involving Random Variables and Their Expectations 434 14.1 Functions of Random Variables. The Transport Formula 441 Bibliography 445 Index 447.
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QA273 .F65 2014  Unknown 
19. The improbability principle : why coincidences, miracles, and rare events happen every day [2014]
 Hand, D. J. (David J.), 1950
 First edition.  New York : Scientific American/Farrar, Straus and Giroux, 2014.
 Description
 Book — xii, 269 pages : illustrations ; 24 cm
 Summary

 The mystery
 A capricious universe
 What is chance?
 The law of inevitability
 The law of truly large numbers
 The law of selection
 The law of the probability lever
 The law of near enough
 The human mind
 Life, the universe, and everything
 How to use the improbability principle
 Epilogue
 Appendix A. Mindnumbingly large and mindbogglingly small
 Appendix B. Rules of chance.
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QA273 .H3545 2014  Unknown 
20. Introduction to imprecise probabilities [2014]
 Chichester, West Sussex : Wiley, 2014.
 Description
 Book — xxvi, 404 pages : illustrations ; 25 cm.
 Summary

In recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience. This will be the first book providing such an introduction, covering core theory and recent developments which can be applied to many application areas. All authors of individual chapters are leading researchers on the specific topics, assuring high quality and uptodate contents. An Introduction to Imprecise Probabilities provides a comprehensive introduction to imprecise probabilities, including theory and applications reflecting the current state if the art. Each chapter is written by experts on the respective topics, including: Sets of desirable gambles; Coherent lower (conditional) previsions; Special cases and links to literature; Decision making; Graphical models; Classification; Reliability and risk assessment; Statistical inference; Structural judgments; Aspects of implementation (including elicitation and computation); Models in finance; Gametheoretic probability; Stochastic processes (including Markov chains); Engineering applications. Essential reading for researchers in academia, research institutes and other organizations, as well as practitioners engaged in areas such as risk analysis and engineering.
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QA273 .I56 2014  Unknown 
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