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  3. General Irreducible Markov Chains and Non-Negative Operators
  • Cited by 465
Publisher:
Cambridge University Press
Online publication date:
September 2009
Print publication year:
1984
Online ISBN:
9780511526237
DOI:
https://doi.org/10.1017/CBO9780511526237
Subjects:
Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
Series:
Cambridge Tracts in Mathematics (83)
Information

Book description

The purpose of this book is to present the theory of general irreducible Markov chains and to point out the connection between this and the Perron-Frobenius theory of nonnegative operators. The author begins by providing some basic material designed to make the book self-contained, yet his principal aim throughout is to emphasize recent developments. The technique of embedded renewal processes, common in the study of discrete Markov chains, plays a particularly important role. The examples discussed indicate applications to such topics as queueing theory, storage theory, autoregressive processes and renewal theory. The book will therefore be useful to researchers in the theory and applications of Markov chains. It could also be used as a graduate-level textbook for courses on Markov chains or aspects of operator theory.

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