Cambridge Tracts in Mathematics Ser.: General Irreducible Markov Chains and Non-Negative Operators by Esa Nummelin (2004, Trade Paperback)
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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 technique of embedded renewal processes, common in the study of discrete Markov chains, plays a particularly important role.