An Introduction to Markov Processes

Softcover Nachdruck of the original 2. Auflage 2014
ISBN: 978-3-662-51782-6
Verlag: Springer

Buch, Englisch, Band 230, 203 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 347 g

Reihe: Graduate Texts in Mathematics

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 2 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.

Zielgruppe

Graduate

Autoren/Hrsg.

Stroock, Daniel W.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

Preface.- Random Walks, a Good Place to Begin.- Doeblin's Theory for Markov Chains.- Stationary Probabilities.- More about the Ergodic Theory of Markov Chains.- Markov Processes in Continuous Time.- Reversible Markov Processes.- A minimal Introduction to Measure Theory.- Notation.- References.- Index.

Über Autor(innen)

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.