Markov Processes for Stochastic Modeling

  • Masaaki Kijima

Table of contents

  1. Front Matter
    Pages i-x
  2. Masaaki Kijima
    Pages 1-23
  3. Masaaki Kijima
    Pages 25-100
  4. Masaaki Kijima
    Pages 101-165
  5. Masaaki Kijima
    Pages 167-241
  6. Masaaki Kijima
    Pages 243-293
  7. Masaaki Kijima
    Pages 295-301
  8. Masaaki Kijima
    Pages 303-312
  9. Masaaki Kijima
    Pages 313-318
  10. Back Matter
    Pages 319-341

About this book


This book presents an algebraic development of the theory of countable state space Markov chains with discrete- and continuous-time parameters. A Markov chain is a stochastic process characterized by the Markov prop­ erty that the distribution of future depends only on the current state, not on the whole history. Despite its simple form of dependency, the Markov property has enabled us to develop a rich system of concepts and theorems and to derive many results that are useful in applications. In fact, the areas that can be modeled, with varying degrees of success, by Markov chains are vast and are still expanding. The aim of this book is a discussion of the time-dependent behavior, called the transient behavior, of Markov chains. From the practical point of view, when modeling a stochastic system by a Markov chain, there are many instances in which time-limiting results such as stationary distributions have no meaning. Or, even when the stationary distribution is of some importance, it is often dangerous to use the stationary result alone without knowing the transient behavior of the Markov chain. Not many books have paid much attention to this topic, despite its obvious importance.


Markov chain Markov process Parameter algebra modeling

Authors and affiliations

  • Masaaki Kijima
    • 1
  1. 1.Graduate School of Systems ManagementUniversity of TsukubaTokyoJapan

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media New York 1997
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-412-60660-1
  • Online ISBN 978-1-4899-3132-0
  • Buy this book on publisher's site