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Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics)

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In this rigorous account the author studies both discrete-time and continuous-time chains. 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 a careful selection of exercises and examples drawn both from theory and practice. This is an ideal text for seminars on random processes or for those that are more oriented towards applications, for advanced undergraduates or graduate students with some background in basic probability theory.

Markov chains are central to the understanding of random processes. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov chains and develops quickly a coherent and rigorous theory whilst showing also how actually to apply it. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and a careful selection of exercises and examples drawn both from theory and practice.
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