An Introduction to Markov Processes

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Springer Science & Business Media, Oct 28, 2013 - Mathematics - 203 pages

This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including students from engineering, economics, physics, and biology. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time processes. Applications are dispersed throughout the book. In addition, a whole chapter is devoted to reversible processes and the use of their associated Dirichlet forms to estimate the rate of convergence to equilibrium. These results are then applied to the analysis of the Metropolis (a.k.a simulated annealing) algorithm.

The corrected and enlarged 2nd edition contains a new chapter in which the author develops computational methods for Markov chains on a finite state space. Most intriguing is the section with a new technique for computing stationary measures, which is applied to derivations of Wilson's algorithm and Kirchoff's formula for spanning trees in a connected graph.

 

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Contents

Random Walks a Good Place to Begin
1
Doeblins Theory for Markov Chains
25
Stationary Probabilities
49
More About the Ergodic Properties of Markov Chains
73
Markov Processes in Continuous Time
99
Reversible Markov Processes
137
A Minimal Introduction to Measure Theory
179
References
199
Index
200
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About the author (2013)

Daniel Stroock has held positions at NYU, the University of Colorado, and MIT. In addition, he has visited and lectured at many universities throughout the world. He has authored several books on analysis and various aspects of probability theory and their application to partial differential equations and differential geometry.

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