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Continuous-Time Markov Chains

An Applications-Oriented Approach

  • Book
  • © 1991

Overview

Authors:
  1. William J. Anderson

    1. Department of Mathematics and Statistics, McGill University, Montreal, Canada

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Part of the book series: Springer Series in Statistics (SSS)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xii
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  2. Transition Functions and Resolvents

    • William J. Anderson
    Pages 1-60

  3. Existence and Uniqueness of Q-Functions

    • William J. Anderson
    Pages 61-91

  4. Examples of Continuous-Time Markov Chains

    • William J. Anderson
    Pages 92-119

  5. More on the Uniqueness Problem

    • William J. Anderson
    Pages 120-154

  6. Classification of States and Invariant Measures

    • William J. Anderson
    Pages 155-203

  7. Strong and Exponential Ergodicity

    • William J. Anderson
    Pages 204-232

  8. Reversibility, Monotonicity, and Other Properties

    • William J. Anderson
    Pages 233-260

  9. Birth and Death Processes

    • William J. Anderson
    Pages 261-291

  10. Population Processes

    • William J. Anderson
    Pages 292-332

  11. Back Matter

    Pages 333-355
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Keywords

About this book

Continuous time parameter Markov chains have been useful for modeling various random phenomena occurring in queueing theory, genetics, demography, epidemiology, and competing populations. This is the first book about those aspects of the theory of continuous time Markov chains which are useful in applications to such areas. It studies continuous time Markov chains through the transition function and corresponding q-matrix, rather than sample paths. An extensive discussion of birth and death processes, including the Stieltjes moment problem, and the Karlin-McGregor method of solution of the birth and death processes and multidimensional population processes is included, and there is an extensive bibliography. Virtually all of this material is appearing in book form for the first time.

Authors and Affiliations

  • Department of Mathematics and Statistics, McGill University, Montreal, Canada

    William J. Anderson

Bibliographic Information

  • Book Title: Continuous-Time Markov Chains

  • Book Subtitle: An Applications-Oriented Approach

  • Authors: William J. Anderson

  • Series Title: Springer Series in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-3038-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1991

  • Softcover ISBN: 978-1-4612-7772-9Published: 18 September 2011

  • eBook ISBN: 978-1-4612-3038-0Published: 06 December 2012

  • Series ISSN: 0172-7397

  • Series E-ISSN: 2197-568X

  • Edition Number: 1

  • Number of Pages: XII, 355

  • Topics: Probability Theory and Stochastic Processes

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