- Includes many results which are published for the first time in a textbook
- Many results are illustrated with simple examples
- Provides an accessible presentation of important ergodicity results of general state Markov chains with many new proof ideas
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- About this Textbook
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This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained, while all the results are carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature.
Part I lays the foundations of the theory of Markov chain on general states-space. Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques. These two parts can serve as a text on general state-space applied Markov chain theory. Although the choice of topics is quite different from what is usually covered, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all these developments without any mathematical background deeper than that needed to study countable state space (very little measure theory is required).
Part III covers advanced topics on the theory of irreducible Markov chains. The emphasis is on geometric and subgeometric convergence rates and also on computable bounds. Some results appeared for a first time in a book and others are original. Part IV are selected topics on Markov chains, covering mostly hot recent developments.
- About the authors
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Randal Douc is a Professor in the CITI Department at Telecom SudParis. His research interests include parameter estimation in general Hidden Markov models and Markov Chain Monte Carlo (MCMC) and sequential Monte Carlo methods.
Eric Moulines is a Professor at Ecole Polytechnique's Applied Mathematics Center (CMAP, UMR Ecole Polytechnique/CNRS).
Pierre Priouret is a Professor at Université Pierre et Marie Curie
Philippe Soulier is a professor at Université de Paris-Nanterre
- Table of contents (23 chapters)
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Markov Chains: Basic Definitions
Pages 3-25
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Examples of Markov Chains
Pages 27-52
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Stopping Times and the Strong Markov Property
Pages 53-74
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Martingales, Harmonic Functions and Poisson–Dirichlet Problems
Pages 75-96
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Ergodic Theory for Markov Chains
Pages 97-115
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Table of contents (23 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Markov Chains
- Authors
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- Randal Douc
- Eric Moulines
- Pierre Priouret
- Philippe Soulier
- Series Title
- Springer Series in Operations Research and Financial Engineering
- Copyright
- 2018
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-319-97704-1
- DOI
- 10.1007/978-3-319-97704-1
- Hardcover ISBN
- 978-3-319-97703-4
- Series ISSN
- 1431-8598
- Edition Number
- 1
- Number of Pages
- XVIII, 757
- Number of Illustrations
- 423 b/w illustrations, 1 illustrations in colour
- Topics
