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 modeling 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. Here, the
authors provide a self-contained introduction to the theory and
details of how the required Lyapunov functions are constructed in
various situations.
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