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  1. Home
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  3. Topics in the Constructive Theory of Countable Markov Chains
  • Cited by 187
  • G. Fayolle, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt, V. A. Malyshev, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt, M. V. Menshikov, Moscow State University
Publisher:
Cambridge University Press
Online publication date:
November 2011
Print publication year:
1995
Online ISBN:
9780511984020
DOI:
https://doi.org/10.1017/CBO9780511984020
Subjects:
Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
Information

Book description

Markov chains are an important idea, related to random walks, which crops up widely in applied stochastic analysis. They are used, for example, in performance modelling and evaluation of computer networks, queuing networks, and telecommunication systems. The main point of the present book is to provide methods, based on the construction of Lyapunov functions, of determining when a Markov chain is ergodic, null recurrent, or transient. These methods can also be extended to the study of questions of stability. Of particular concern are reflected random walks and reflected Brownian motion. The authors provide not only a self-contained introduction to the theory but also details of how the required Lyapunov functions are constructed in various situations.

Reviews

Review of the hardback:‘The monograph is an excellent piece of work that gives an original and alternative view on countable Markov chains.’

Source: Mededelingen van het Wiskundig Genootschap

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