Continuous Time Markov Processes
：An Introduction
( Graduate Studies in Mathematics )
Publication subTitle ：An Introduction
Publication series ：Graduate Studies in Mathematics
Author： Thomas M. Liggett
Publisher： American Mathematical Society
Publication year： 2010
E-ISBN: 9781470411756
P-ISBN(Paperback): 9780821849491
Subject： O211.62 Markov process
Keyword： Probability and Statistics
Language： ENG
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Continuous Time Markov Processes
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. This is a textbook for a graduate course that can follow one that covers basic probabilistic limit theorems and discrete time processes.
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