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  • Textbook
  • © 1976

Denumerable Markov Chains

with a chapter of Markov Random Fields by David Griffeath

Part of the book series: Graduate Texts in Mathematics (GTM, volume 40)

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  • ISBN: 978-1-4684-9455-6
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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xii
  2. Prerequisites From Analysis

    • John G. Kemeny, J. Laurie Snell, Anthony W. Knapp
    Pages 1-39
  3. Stochastic Processes

    • John G. Kemeny, J. Laurie Snell, Anthony W. Knapp
    Pages 40-57
  4. Martingales

    • John G. Kemeny, J. Laurie Snell, Anthony W. Knapp
    Pages 58-78
  5. Properties of Markov Chains

    • John G. Kemeny, J. Laurie Snell, Anthony W. Knapp
    Pages 79-105
  6. Transient Chains

    • John G. Kemeny, J. Laurie Snell, Anthony W. Knapp
    Pages 106-129
  7. Recurrent Chains

    • John G. Kemeny, J. Laurie Snell, Anthony W. Knapp
    Pages 130-165
  8. Introduction to Potential Theory

    • John G. Kemeny, J. Laurie Snell, Anthony W. Knapp
    Pages 166-190
  9. Transient Potential Theory

    • John G. Kemeny, J. Laurie Snell, Anthony W. Knapp
    Pages 191-240
  10. Recurrent Potential Theory

    • John G. Kemeny, J. Laurie Snell, Anthony W. Knapp
    Pages 241-322
  11. Transient Boundary Theory

    • John G. Kemeny, J. Laurie Snell, Anthony W. Knapp
    Pages 323-400
  12. Recurrent Boundary Theory

    • John G. Kemeny, J. Laurie Snell, Anthony W. Knapp
    Pages 401-424
  13. Introduction to Random Fields

    • David Griffeath
    Pages 425-458
  14. Back Matter

    Pages 459-484

About this book

With the first edition out of print, we decided to arrange for republiĀ­ cation of Denumerrible Markov Ohains with additional bibliographic material. The new edition contains a section Additional Notes that indicates some of the developments in Markov chain theory over the last ten years. As in the first edition and for the same reasons, we have resisted the temptation to follow the theory in directions that deal with uncountable state spaces or continuous time. A section entitled Additional References complements the Additional Notes. J. W. Pitman pointed out an error in Theorem 9-53 of the first edition, which we have corrected. More detail about the correction appears in the Additional Notes. Aside from this change, we have left intact the text of the first eleven chapters. The second edition contains a twelfth chapter, written by David Griffeath, on Markov random fields. We are grateful to Ted Cox for his help in preparing this material. Notes for the chapter appear in the section Additional Notes. J.G.K., J.L.S., A.W.K.

Keywords

  • Brownian motion
  • Chains
  • Markov
  • Markov chain
  • Markov property
  • Martingale
  • Random Walk
  • Random variable
  • Stochastic processes
  • measure theory
  • stochastic process

Authors and Affiliations

  • Dartmouth College, Hanover, Germany

    John G. Kemeny

  • Department of Mathematics, Dartmouth College, Hanover, Germany

    J. Laurie Snell

  • Department of Mathematics, State University of New York, Stony Brook, USA

    Anthony W. Knapp

Bibliographic Information

  • Book Title: Denumerable Markov Chains

  • Book Subtitle: with a chapter of Markov Random Fields by David Griffeath

  • Authors: John G. Kemeny, J. Laurie Snell, Anthony W. Knapp

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-9455-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1976

  • Hardcover ISBN: 978-0-387-90177-0

  • Softcover ISBN: 978-1-4684-9457-0

  • eBook ISBN: 978-1-4684-9455-6

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XII, 484

  • Additional Information: Originally published by Van Nostrand Publishing Company, 1966

  • Topics: Probability Theory, Analysis

Buying options

eBook USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-1-4684-9455-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 79.99
Price excludes VAT (USA)
Hardcover Book USD 99.99
Price excludes VAT (USA)