Overview
- 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
Part of the book series: Springer Series in Operations Research and Financial Engineering (ORFE)
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Table of contents (23 chapters)
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Front Matter
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Foundations
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Front Matter
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Irreducible Chains: Basics
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Front Matter
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Irreducible Chains: Advanced Topics
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Front Matter
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Irreducible Chains: Advanced Topics
Keywords
About this book
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 deeperthan 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.
Authors and Affiliations
About the authors
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
Bibliographic Information
Book Title: Markov Chains
Authors: Randal Douc, Eric Moulines, Pierre Priouret, Philippe Soulier
Series Title: Springer Series in Operations Research and Financial Engineering
DOI: https://doi.org/10.1007/978-3-319-97704-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-97703-4Published: 03 January 2019
eBook ISBN: 978-3-319-97704-1Published: 11 December 2018
Series ISSN: 1431-8598
Series E-ISSN: 2197-1773
Edition Number: 1
Number of Pages: XVIII, 757
Number of Illustrations: 423 b/w illustrations, 1 illustrations in colour