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Finite Markov Chains

Posted on 2011-01-02




Name:Finite Markov Chains
ASIN/ISBN:0387901922
Publisher:Sprin..ger 1976
Publish Date:0387901922 , 3540901922
Pages:244 Pages
File size:2 Mb
Publisher: Sprin..ger 1976
Pages: 244 Pages
ISBN: 0387901922 , 3540901922
File Size: 2 MB
Other Info: DJVU
   Finite Markov Chains

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By John G. Kemeny, J. Laurie Snell

The basic concepts of Markov chains were introduced by A. A. Markov in 1907. Since that time Markov chain theory has been developed by a number of leading mathematicians. It is only in very recent times that the importance of Markov chain theory to the social and biological sciences has become recognized. This new interest has, we believe, produced a real need for a treatment, in English, of the basic ideas of .

By restricting our attention to finite chains, we are able to give quite a complete treatment and in such a way that a minimum amount of mathematical background is needed. For example, we have written the book in such a way that it can be used in an undergraduate probability course, as well as a reference book for workers in fields outside of mathematics.

The restriction of this book to finite chains has made it possible to give simple, closed-form matrix expressions for many quantities usually given as series. It is shown that it suffices for all types of problems to consider just two types of Markov chains, namely absorbing and ergodic chains. A "fundamental matrix" is developed for each type of chain, and the other interesting quantities are obtained from the fundamental matrices by elementary matrix operations.

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