Stochastic Processes

A nonmeasure theoretic introduction to stochastic processes. Considers its diverse range of applications and provides readers with probabilistic intuition and insight in thinking about problems. This revised edition contains additional material on compound Poisson random variables including an identity which can be used to efficiently compute moments; a new chapter on Poisson approximations; and coverage of the mean time spent in transient states as well as examples relating to the Gibb′s sampler, the Metropolis algorithm and mean cover time in star graphs. Numerous exercises and problems have been added throughout the text.

Spis treści:
Preliminaries.
The Poisson Process.
Renewal Theory.
Markov Chains.
Continuous–Time Markov Chains.
Martingales.
Random Walks.
Brownian Motion and Other Markov Processes.
Stochastic Order Relations.
Poisson Approximations.
Answers and Solutions to Selected Problems.
Index.