Daniel W. Stroock

An Introduction to Markov Processes

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Graduate Texts in Mathematics 230
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-642-40522-8
• 2. Aufl.
• Seitenzahl: 224
• Erscheinungstermin: 8. November 2013
• Englisch
• Abmessung: 241mm x 160mm x 18mm
• Gewicht: 476g
• ISBN-13: 9783642405228
• ISBN-10: 3642405223
• Artikelnr.: 39158164

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

From the reviews:
"The book under review ... provides an excellent introduction to the theory of Markov processes ... . An abstract mathematical setting is given in which Markov processes are then defined and thoroughly studied. Because of this the book will basically be of interest to mathematicians and those who have at least a good knowledge of undergraduate analysis and probability theory. ... The proofs are clearly written and explanations are not too concise which makes this book indeed very useful for a graduate course." (Stefaan De Winter, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)