Dirichlet Forms and Markov Processes (Mathematical Library Series, Vol 23): Masatoshi Fukushima

Description

A long time has passed since an intimate relationship between classical potential theory and Brownian motion was revealed. In the meantime, both potential theory and the theory of Markov processes have developed rather separately. In particular, Beurling and Deny formulated in 1959, the theory of Dirichlet space-an axiomatic extension of classical Dirichlet integrals in the direction of Markovian semigroups. Almost simultaneously. Hunt and Dynkin introduced the notions of the Hunt process and the standard process on which a probabilistic potential theory was built. This book is an attempt to unify these two theories. By unification the theory of Markov processes bears an intrinsic analytical tool of great use, while the theory of Dirichlet spaces acquires a deep probabilistic structure. Part I of this book contains an introductory and comprehensive account of the theory of Dirichlet forms, which is fully applied to the study of Markov processes in Part II. A brief summary at the beginning of each chapter and simple examples presented in many sections serve to help you in interpreting the text.

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