Continuous time Markov processes : an introduction / Thomas M. Liggett.

Includes bibliographical references and index.

One-dimensional Brownian motion -- Continuous time Markov chains -- Feller processes -- Interacting particle systems -- Stochastic integration -- Multi-dimensional Brownian motion and the Dirichlet problem.

'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.