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Markov Chains

Gibbs Fields, Monte Carlo Simulation, and Queues

  • Textbook
  • © 1999

Overview

Authors:
  1. Pierre Brémaud

    1. Laboratoire des Signaux et Systèmes, CNRS-ESE, Gif-sur-Yvette, France

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Probability Review

    • Pierre Brémaud
    Pages 1-52

  3. Discrete-Time Markov Models

    • Pierre Brémaud
    Pages 53-93

  4. Recurrence and Ergodicity

    • Pierre Brémaud
    Pages 95-124

  5. Long Run Behavior

    • Pierre Brémaud
    Pages 125-165

  6. Lyapunov Functions and Martingales

    • Pierre Brémaud
    Pages 167-193

  7. Eigenvalues and Nonhomogeneous Markov Chains

    • Pierre Brémaud
    Pages 195-251

  8. Gibbs Fields and Monte Carlo Simulation

    • Pierre Brémaud
    Pages 253-322

  9. Continuous-Time Markov Models

    • Pierre Brémaud
    Pages 323-368

  10. Poisson Calculus and Queues

    • Pierre Brémaud
    Pages 369-416

  11. Back Matter

    Pages 417-445
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Keywords

About this book

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.

Authors and Affiliations

  • Laboratoire des Signaux et Systèmes, CNRS-ESE, Gif-sur-Yvette, France

    Pierre Brémaud

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