Cover image for Markov chains
Title:
Markov chains
Personal Author:
Publication Information:
New York, NY : Cambridge Univ Press, 1997
ISBN:
9780521481816
Subject Term:

Available:*

Library
Item Barcode
Call Number
Material Type
Item Category 1
Status
Searching...
30000003895145 QA274.7 N68 1997 Open Access Book Book
Searching...

On Order

Summary

Summary

Markov chains are central to the understanding of random processes. This is not only because they pervade the applications of random processes, but also because one can calculate explicitly many quantities of interest. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov chains and quickly develops a coherent and rigorous theory whilst showing also how actually to apply it. Both discrete-time and continuous-time chains are studied. A distinguishing feature is an introduction to more advanced topics such as martingales and potentials in the established context of Markov chains. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and exercises and examples drawn both from theory and practice. It will therefore be an ideal text either for elementary courses on random processes or those that are more oriented towards applications.


Reviews 1

Choice Review

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


Table of Contents

Introduction
1 Discrete-time Markov chains
2 Continuous-time Markov chains I
3 Continuous-time Markov chains II
4 Further theory
5 Applications
Appendix
Probability and measure
Index