© 2006

Cycle Representations of Markov Processes


  • Excellent pedagogical methods

  • Promotes original ideas and methods and developes intuition

  • Chapter summaries as well as a number of detailed illustrations included


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

Table of contents

About this book


Markov chain Markov process Markov processes Stochastic processes random walk stochastic process

Authors and affiliations

  1. 1.Department of MathematicsAristotle UniversityThessalonikiGreece

Bibliographic information

  • Book Title Cycle Representations of Markov Processes
  • Authors Sophia L. Kalpazidou
  • Series Title Stochastic Modelling and Applied Probability
  • DOI
  • Copyright Information Springer Science+Business Media, Inc. 2006
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-29166-6
  • Softcover ISBN 978-1-4419-2121-5
  • eBook ISBN 978-0-387-36081-2
  • Series ISSN 0172-4568
  • Edition Number 2
  • Number of Pages XX, 304
  • Number of Illustrations 17 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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From the reviews of the second edition:

"The first edition of this book [S. Kalpazidou, Cycle representations of Markov processes, Springer, New York, 1995; MR1336140 (96g:60002)] has been reviewed by this reviewer. This second edition amplifies Part I of the first edition, which consisted of 7 chapters, by adding four chapters: Chapter 8. Cycloid Markov processes; Chapter 9. Markov processes on Banach spaces on cycles; Chapter 10. The cycle measures; Chapter 11. Wide-ranging interpretations of the cycle representations of Markov processes. Also, there is a new Section 3.6 devoted to induced circuit chains in Part I, and a new Section 1.4 on Derriennic recurrence criteria in terms of weighted circuits in Part II. Besides, improvements have been introduced at different places (without completely eliminating linguistic slips).

The reviewer is glad that this second edition confirms his expectations concerning the applicability potential of the cycle representation topic. The book under review is indeed mainly motivated by the many applications of cycle representations which occurred in different fields, after the publication of the first edition. "   (M. Iosifescu, Mathematical Reviews)

"The main purpose of the second edition … is to give systematic and unified exposition of stochastic processes of the Markovian type, homogeneous and with either discrete or continuous parameter, which, under an additional assumption concerning the existence of invariant measures, can be defined by directed cycles or circuits. … The book will be useful for experts in representation theory of Markov processes." (Anatoliy Swishchuk, Zentralblatt MATH, Vol. 1113 (15), 2007)