This book contains an introductory and comprehensive account of the theory of (symmetric) Dirichlet forms. Moreover this analytic theory is unified with the probabilistic potential theory based on symmetric Markov processes and developed further in conjunction with the stochastic analysis based on additive functional. Since the publication of the first edition in 1994, this book has attracted constant interests from readers and is by now regarded as a standard reference for the theory of Dirichlet forms. For the present second edition, the authors not only revised the existing text, but also added sections on capacities and Sobolev type inequalities, irreducible recurrence and ergodicity, recurrence and Poincaré type inequalities, the Donsker-Varadhan type large deviation principle, as well as several new exercises with solutions. The book addresses to researchers and graduate students who wish to comprehend the area of Dirichlet forms and symmetric Markov processes.

Autorentext

Masatoshi Fukushima, Osaka University, Japan; Yoichi Oshima, Kumamoto University, Japan; Masayoshi Takeda, Tohoku University, Japan.

Zusammenfassung

"The theory is constantly illustrated by a variety of interesting examples which follow chapter after chapter. The book appears to be the best reference on this important subject at the interface between functional analysis and probability theory." Mathematical Reviews

"The authors made this second edition more suitable as a textbook by converting the problems in the first edition into exercises and by adding many new exercises." Zentralblatt für Mathematik