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Cycle Representations of Markov Processes

  • Book
  • © 1995

Overview

Authors:
  1. Sophia L. Kalpazidou

    1. Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, Greece

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Part of the book series: Stochastic Modelling and Applied Probability (SMAP, volume 28)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xv
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  2. Fundamentals of the Cycle Representations of Markov Processes

    1. Front Matter

      Pages 1-1
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    2. Directed Circuits

      • Sophia L. Kalpazidou
      Pages 3-16

    3. Genesis of Markov Chains by Circuits: The Circuit Chains

      • Sophia L. Kalpazidou
      Pages 17-27

    4. Cycle Representations of Recurrent Denumerable Markov Chains

      • Sophia L. Kalpazidou
      Pages 28-46

    5. Circuit Representations of Finite Recurrent Markov Chains

      • Sophia L. Kalpazidou
      Pages 47-63

    6. Continuous Parameter Circuit Processes with Finite State Space

      • Sophia L. Kalpazidou
      Pages 64-81

    7. Spectral Theory of Circuit Processes

      • Sophia L. Kalpazidou
      Pages 82-89

    8. Higher-Order Circuit Processes

      • Sophia L. Kalpazidou
      Pages 90-117

  3. Applications of the Cycle Representations

    1. Front Matter

      Pages 119-119
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    2. Stochastic Properties in Terms of Circuits

      • Sophia L. Kalpazidou
      Pages 121-128

    3. Lévy’s Theorem Concerning Positiveness of Transition Probabilities

      • Sophia L. Kalpazidou
      Pages 129-134

    4. The Rotational Theory of Markov Processes

      • Sophia L. Kalpazidou
      Pages 135-166

  4. Back Matter

    Pages 167-194
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Keywords

About this book

This book provides new insight into Markovian dependence via the cycle decompositions. It presents a systematic account of a class of stochastic processes known as cycle (or circuit) processes - so-called because they may be defined by directed cycles. An important application of this approach is the insight it provides to electrical networks and the duality principle of networks. This expanded second edition adds new advances, which reveal wide-ranging interpretations of cycle representations such as homologic decompositions, orthogonality equations, Fourier series, semigroup equations, and disintegration of measures. The text includes chapter summaries as well as a number of detailed illustrations.

Reviews

"This book is an excellent state-of-the-art survey of the principal trends to cycle processes theory." - M. Csörgö, Carleton University, Ottawa

Authors and Affiliations

  • Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Sophia L. Kalpazidou

Bibliographic Information

  • Book Title: Cycle Representations of Markov Processes

  • Authors: Sophia L. Kalpazidou

  • Series Title: Stochastic Modelling and Applied Probability

  • DOI: https://doi.org/10.1007/978-1-4757-3929-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1995

  • eBook ISBN: 978-1-4757-3929-9Published: 29 June 2013

  • Series ISSN: 0172-4568

  • Series E-ISSN: 2197-439X

  • Edition Number: 1

  • Number of Pages: XV, 194

  • Number of Illustrations: 4 b/w illustrations

  • Additional Information: Originally published in the series: Applications Mathematics

  • Topics: Probability Theory and Stochastic Processes, Combinatorics

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