Continuous time Markov processes
Subtitle: an introduction
By: Thomas M. Liggett
Series: Graduate studies in mathematics -- v. 113; Graduate studies in mathematics -- v. 113.
Publisher: American Mathematical Society
Published: 2010
Place of publication: Providence, R.I
Language: eng
Number of pages: 271
ISBN-13: 9780821849491
Description: "Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes and applies this theory to various special examples. The initial chapter is devoted to the most important classical example--one-dimensional Brownian motion. This, together with a chapter on continuous time Markov chains, provides the motivation for the general setup based on semigroups and generators. Chapters on stochastic calculus and probabilistic potential theory give an introduction to some of the key areas of application of Brownian motion and its relatives. A chapter on interacting particle systems treats a more recently developed class of Markov processes that have as their origin problems in physics and biology."--Publisher's description.
Notes: Includes bibliographical references and index.
Table of contents: title: One-dimensional Brownian motion; title: Continuous time Markov chains; title: Feller processes; title: Interacting particle systems; title: Stochastic integration; title: Multi-dimensional Brownian motion and the Dirichlet problem.