Stochastic Modelling and Applied Probability

Cycle Representations of Markov Processes

Authors: Kalpazidou, Sophia L.

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Reviews

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)


Table of contents (14 chapters)

Table of contents (14 chapters)
  • Directed Circuits

    Pages 3-16

  • Genesis of Markov Chains by Circuits: The Circuit Chains

    Pages 17-28

  • Cycle Representations of Recurrent Denumerable Markov Chains

    Pages 29-53

  • Circuit Representations of Finite Recurrent Markov Chains

    Pages 55-72

  • Continuous Parameter Circuit Processes with Finite State Space

    Pages 73-91

Buy this book

eBook $129.00
price for USA in USD (gross)
  • ISBN 978-0-387-36081-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-0-387-29166-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.99
price for USA in USD
  • ISBN 978-1-4419-2121-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Cycle Representations of Markov Processes
Authors
Series Title
Stochastic Modelling and Applied Probability
Series Volume
28
Copyright
2006
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-36081-2
DOI
10.1007/0-387-36081-6
Hardcover ISBN
978-0-387-29166-6
Softcover ISBN
978-1-4419-2121-5
Series ISSN
0172-4568
Edition Number
2
Number of Pages
XX, 304
Number of Illustrations
17 b/w illustrations
Additional Information
Originally published in the series: Applications Mathematics
Topics