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Markov Chains

Gibbs Fields, Monte Carlo Simulation, and Queues

  • Pierre Brémaud

Part of the Texts in Applied Mathematics book series (TAM, volume 31)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Pierre Brémaud
    Pages 1-52
  3. Pierre Brémaud
    Pages 53-93
  4. Pierre Brémaud
    Pages 95-124
  5. Pierre Brémaud
    Pages 125-165
  6. Pierre Brémaud
    Pages 167-193
  7. Pierre Brémaud
    Pages 195-251
  8. Pierre Brémaud
    Pages 253-322
  9. Pierre Brémaud
    Pages 323-368
  10. Pierre Brémaud
    Pages 369-416
  11. Back Matter
    Pages 417-445

About this book

Introduction

In this book, the author begins with the elementary theory of Markov chains and very progressively brings the reader to the more advanced topics. He gives a useful review of probability that makes 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 are slowly and carefully developed, in order to make self-study easier. The author treats the classic topics of Markov chain theory, both in discrete time and continuous time, as well as the connected topics such as finite Gibbs fields, nonhomogeneous Markov chains, discrete- time regenerative processes, Monte Carlo simulation, simulated annealing, and queuing theory. 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.

Keywords

Markov Markov Chains Markov model Martingale Monte Carlo Simulation Stochastic model Stochastic modelling electrical engineering ergodicity linear optimization modeling operations research regenerative process simulation stochastic process

Authors and affiliations

  • Pierre Brémaud
    • 1
  1. 1.Laboratoire des Signaux et SystèmesCNRS-ESEGif-sur-YvetteFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3124-8
  • Copyright Information Springer-Verlag New York 1999
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3131-3
  • Online ISBN 978-1-4757-3124-8
  • Series Print ISSN 0939-2475
  • Buy this book on publisher's site
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