Topics in the Constructive Theory of Countable Markov Chains

by G. Fayolle , V. A. Malyshev , M. V. Menshikov

• ISBN13: 9780521064477
• ISBN10: 0521064473
• Edition: 1st
• Format: Paperback
• Copyright: 2008-06-05
• Publisher: Cambridge University Press

Summary

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, which are on the whole original and new, 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.

Table of Contents

Introduction and history

Preliminaries

General criteria

Explicit construction of Lyapunov functions

Ideology of induced chains

Random walks in two dimensional complexes

Stability

Exponential convergence and analyticity for ergodic Markov chains

Bibliography

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