Markov Chains : Gibbs Fields, Monte Carlo Simulation and Queues / by Pierre Brémaud.

Format:

Book

Author/Creator:

Brémaud, Pierre, author.

Contributor:

SpringerLink (Online service)

Series:

Mathematics and Statistics (SpringerNature-11649)

Texts in applied mathematics 0939-2475 ; 31.

Texts in Applied Mathematics, 0939-2475 ; 31

Language:

English

Subjects (All):

Probabilities.

Operations research.

Decision making.

Electrical engineering.

Probability Theory and Stochastic Processes.

Operations Research/Decision Theory.

Electrical Engineering.

Local Subjects:

Probability Theory and Stochastic Processes.

Operations Research/Decision Theory.

Electrical Engineering.

Physical Description:

1 online resource (XVI, 557 pages) : 93 illustrations.

Edition:

Second edition 2020.

Contained In:

Springer Nature eBook

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2020.

System Details:

text file PDF

Summary:

This 2nd edition is a thoroughly revised and augmented version of the book with the same title published in 1999. The author begins with the elementary theory of Markov chains and very progressively brings the reader to more advanced topics. He gives a useful review of probability, making the book self-contained, and provides an appendix with detailed proofs of all the prerequisites from calculus, algebra, and number theory. A number of carefully chosen problems of varying difficulty are proposed at the close of each chapter, and the mathematics is slowly and carefully developed, in order to make self-study easier. The book treats the classical topics of Markov chain theory, both in discrete time and continuous time, as well as connected topics such as finite Gibbs fields, nonhomogeneous Markov chains, discrete-time regenerative processes, Monte Carlo simulation, simulated annealing, and queuing theory. The main additions of the 2nd edition are the exact sampling algorithm of Propp and Wilson, the electrical network analogy of symmetric random walks on graphs, mixing times and additional details on the branching process. The structure of the book has been modified in order to smoothly incorporate this new material. Among the features that should improve reader-friendliness, the three main ones are: a shared numbering system for the definitions, theorems and examples; the attribution of titles to the examples and exercises; and the blue highlighting of important terms. The result is an up-to-date textbook on stochastic processes. Students and researchers in operations research and electrical engineering, as well as in physics and biology, will find it very accessible and relevant.

Contents:

Preface

1 Probability Review

2 Discrete-Time Markov Chains

3 Recurrence and Ergodicity

4 Long-Run Behavior

5 Discrete-Time Renewal Theory

6 Absorption and Passage Times

7 Lyapunov Functions and Martingales

8 Random Walks on Graphs

9 Convergence Rates

10 Markov Fields on Graphs

11 Monte Carlo Markov Chains

12 Non-homogeneous Markov Chains

13 Continuous-Time Markov Chains

14 Markovian Queueing Theory

Appendices

Bibliography

Index.

Other Format:

Printed edition:

ISBN:

978-3-030-45982-6

9783030459826

Access Restriction:

Restricted for use by site license.