Dirichlet Forms and Symmetric Markov Processes

Japanese mathematicians Fukushima (Osaka U.), Yoichi Oshima (Kumamato U.), and Masayoshi Takeda (Tohoku U.) begin with an introductory and comprehensive account of the theory of (symmetric) Dirichlet forms, which they explain as an axiomatic extension of the classical Dirichlet integrals in the direction of Markovian semigroups. For this they assume readers to have completed a first course in functional analysis. Then they integrate this analytic theory with the probabilistic potential theory based on symmetric Markov processes, and develop it further in conjunction with stochastic analysis based on the additive functionals. Appendices provide the necessary background for that material. Some sections from the 1994 first edition have been removed for this second, and new sections added on capacities and Sobolev type inequalities, irreducible recurrence and ergodicity, recurrence and Poincare type inequalities, and Donsker-Varadhan type large deviation principles. Annotation c2011 Book News, Inc., Portland, OR (booknews.com)

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