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# Markov chains

Author: J R Norris Cambridge, UK ; New York : Cambridge University Press, 1998. Cambridge series on statistical and probabilistic mathematics. Print book : English : 1st pbk. edView all editions and formats Publisher Description (unedited publisher data) 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.  Read more... (not yet rated) 0 with reviews - Be the first.

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Material Type: Internet resource Book, Internet Resource J R Norris Find more information about: J R Norris 0521481813 9780521481816 0521633966 9780521633963 35043455 xvi, 237 pages : illustrations ; 26 cm. 1. Discrete-time Markov chains. 1.1 Definition and basic properties. 1.2 Class structure. 1.3 Hitting times and absorption probabilities. 1.4 Strong Markov property. 1.5 Recurrence and transience. 1.6 Recurrence and transience of random walks. 1.7 Invariant distributions. 1.8 Convergence to equilibrium. 1.9 Time reversal. 1.10 Ergodic theorem. 1.11 Appendix: Recurrence relations. 1.12 Appendix: Asymptotics for n! -- 2. Continuous-time Markov chains I. 2.1 Q-matrices and their exponentials. 2.2 Continuous-time random processes. 2.3 Some properties of the exponential distribution. 2.4 Poisson processes. 2.5 Birth processes. 2.6 Jump chain and holding times. 2.7 Explosion. 2.8 Forward and backward equations. 2.9 Non-minimal chains. 2.10 Appendix: Matrix exponentials -- 3. Continuous-time Markov chains II. 3.1 Basic properties. 3.2 Class structure. 3.3 Hitting times and absorption probabilities. 3.4 Recurrence and transience. 3.5 Invariant distributions. Cambridge series on statistical and probabilistic mathematics. J.R. Norris.

### Abstract:

A textbook for students with some background in probability that develops quickly a rigorous theory of Markov chains and shows how actually to apply it, e.g. to simulation, economics, optimal  Read more...

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'This is an admirable book, treating the topic with mathematical rigour and clarity, mixed with helpful informality; and emphasising numerous applications to a wide range of subjects.' D. V. Lindley, Read more...

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