Topics in the Constructive Theory of Countable Markov Chains

Markov chains are an important idea, related to random walks, which crops up widely in applied stochastic analysis. They are used for such applications as performance modelling and evaluation of computer networks, queuing networks and telecommunication systems. The point of this 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.