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© 2014

An Introduction to Markov Processes

Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 230)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Daniel W. Stroock
    Pages 1-23
  3. Daniel W. Stroock
    Pages 25-47
  4. Daniel W. Stroock
    Pages 49-71
  5. Daniel W. Stroock
    Pages 99-136
  6. Daniel W. Stroock
    Pages 137-177
  7. Daniel W. Stroock
    Pages 179-198
  8. Back Matter
    Pages 199-203

About this book

Introduction

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.

Keywords

60-01, 60J10, 60J27, 60J28, 37L40 Markov chains ergodic theory reversible Markov chains

Authors and affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

About the authors

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.

Bibliographic information

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