© 1995

Cycle Representations of Markov Processes


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

Table of contents

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

    1. Front Matter
      Pages 1-1
    2. Sophia L. Kalpazidou
      Pages 3-16
    3. Sophia L. Kalpazidou
      Pages 82-89
    4. Sophia L. Kalpazidou
      Pages 90-117
  3. Applications of the Cycle Representations

    1. Front Matter
      Pages 119-119
    2. Sophia L. Kalpazidou
      Pages 121-128
    3. Sophia L. Kalpazidou
      Pages 135-166
  4. Back Matter
    Pages 167-194

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.


Markov chain Markov process Markov processes Moment Parameter stochastic processes

Authors and affiliations

  1. 1.Department of MathematicsAristotle University of ThessalonikiThessalonikiGreece

Bibliographic information

  • Book Title Cycle Representations of Markov Processes
  • Authors Sophia L. Kalpazidou
  • Series Title Stochastic Modeling and Applied Probability
  • DOI
  • Copyright Information Springer-Verlag New York 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-94363-3
  • Softcover ISBN 978-1-4757-3931-2
  • eBook ISBN 978-1-4757-3929-9
  • Series ISSN 0172-4568
  • Edition Number 1
  • Number of Pages XV, 194
  • Number of Illustrations 4 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published in the series: Applications Mathematics
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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"This book is an excellent state-of-the-art survey of the principal trends to cycle processes theory." - M. Csörgö, Carleton University, Ottawa