Markov chains /

In this interesting and useful book devoted exclusively to Markov chains, Norris introduces many difficult concepts and key ideas through illustrative examples. In addition to mathematical maturity, the reader will need a course in elementary probability to gain a sound understanding of the material. Chapter 1 discusses the theory of discrete-time Markov chains and forms the basis of all that follows, and chapter 2 also treats continuous-time chains and includes Poisson processes, birth processes, and other chains with finite state space. Chapter 3 reviews continuous-time Markov Chains, making it easier to follow the concepts and key ideas by analogy. In chapter 4 Norris offers some of the ideas crucial to the advanced study of Markov processes in the context of simple Markov chains, such as martingales, potential theory, Brownian motion, and electrical networks. The next chapter is devoted exclusively to applications of Markov chains to biological models, decision processes, queuing models, etc. The last chapter serves as an appendix and includes some of the basic notions of probability and measure used in earlier chapters. Norris has made great efforts, through illustrative examples and explanations, to present with great clarity otherwise difficult and complex concepts and ideas. A readable, erudite, and invaluable contribution to the study of Markov chains. Useful subject index; small reference list. Highly recommended. Upper-division undergraduate and graduate students. D. V. Chopra; Wichita State University