Probability and Statistics by Example

Volume 2, Markov Chains: A Primer in Random Processes and Their Applications

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Hardcover | 24 April 2008

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498 Pages

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Probability and Statistics are as much about intuition and problem solving as they are about theorem proving. Because of this, students can find it very difficult to make a successful transition from lectures to examinations to practice, since the problems involved can vary so much in nature. Since the subject is critical in many modern applications such as mathematical finance, quantitative management, telecommunications, signal processing, bioinformatics, as well as traditional ones such as insurance, social science andengineering, the authors have rectified deficiencies in traditional lecture-based methods by collecting together a wealth of exercises with complete solutions, adapted to needs and skills of students. Following on from the success of Probability and Statistics by Example: Basic Probability and Statistics, the authors here concentrate on random processes, particularly Markov processes, emphasising modelsrather than general constructions. Basic mathematical facts are supplied as and when they are needed andhistorical information is sprinkled throughout.

Industry Reviews

'In this book, one can find a well-balanced mix of clearly explained theory, several classical and interesting examples which complement and integrate the theory discussed, as well as thought-provoking quotations and humorous sentences which make reading this book very pleasant. ... A particular feature is the presence of worked examples which are aimed at giving explicit guidance about how to make the transition form the theory to the practical issue of solving problems. The results presented are always worked out in detail in a style that is never dry but full of hints about the properties and devices used as well as illustrative pictures to stimulate the reader's attention and insight. ... The title might lead someone to think that this book is merely an introduction, however it is not only for the beginner.' Mathematical Reviews
'Following on from the success of Probability and Statistics by Example: Basic Probability and Statistics, the authors here concentrate on random processes, particularly Markov processes, emphasising models rather than general constructions. Basic mathematical facts are supplied as and when they are needed and historical information is sprinkled throughout.' L'Enseignement Mathematique
'I enjoyed reading this book a great deal ... it is a great way to flesh out the general theory with concrete examples and applications.' MAA Reviews

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Preface	p. vii
Discrete-time Markov chains	p. 1
The Markov property and its immediate consequences	p. 1
Class division	p. 17
Hitting times and probabilities	p. 26
Strong Markov property	p. 35
Recurrence and transience: definitions and basic facts	p. 39
Recurrence and transience: random walks on lattices	p. 45
Equilibrium distributions: definitions and basic facts	p. 52
Positive and null recurrence	p. 58
Convergence to equilibrium. Long-run proportions	p. 70
Detailed balance and reversibility	p. 80
Controlled and partially observed Markov chains	p. 89
Geometric algebra of Markov chains, I	p. 99
Geometric algebra of Markov chains, II	p. 116
Geometric algebra of Markov chains, III	p. 130
Large deviations for discrete-time Markov chains	p. 138
Examination questions on discrete-time Markov chains	p. 155
Continuous-time Markov chains	p. 185
Q-matrices and transition matrices	p. 185
Continuous-time Markov chains: definitions and basic constructions	p. 196
The Poisson process	p. 210
Inhomogeneous Poisson process	p. 231
Birth-and-death process. Explosion	p. 240
Continuous-time Markov chains with countably many states	p. 250
Hitting times and probabilities. Recurrence and transience	p. 266
Convergence to an equilibrium distribution. Reversibility	p. 283
Applications to queueing theory. Markovian queues	p. 291
Examination questions on continuous-time Markov chains	p. 308
Statistics of discrete-time Markov chains	p. 349
Introduction	p. 349
Likelihood functions, 1. Maximum likelihood estimators	p. 357
Consistency of estimators. Various forms of convergence	p. 366
Likelihood functions, 2. Whittle's formula	p. 390
Bayesian analysis of Markov chains: prior and posterior distributions	p. 401
Elements of control and information theory	p. 415
Hidden Markov models, 1. State estimation for Markov chains	p. 434
Hidden Markov models, 2. The Baum-Welch learning algorithm	p. 451
Generalisations of the Baum-Welch algorithm	p. 461
Epilogue: Andrei Markov and his Time	p. 479
Bibliography	p. 483
Index	p. 485
Table of Contents provided by Ingram. All Rights Reserved.

Probability and Statistics by Example

Volume 2, Markov Chains: A Primer in Random Processes and Their Applications

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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