Fukushima M., Oshima Y., Takeda M. Dirichlet forms and symmetric Markov processes

2nd Edition. — De Gruyter, 2010. — 501 p. — (De Gruyter Studies in Mathematics 19). — ISBN: 978-3-11-021808-4.Part I of this book contains an introductory and comprehensive account of the theory of (symmetric) Dirichlet forms – an axiomatic extension of the classical Dirichlet integrals in the direction of Markovian semigroups. In Part II, 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 the additive functionals.
We are pleased that our book has attracted constant interests of readers since its publication in 1994. A year ago, Professor Niels Jacob of Swansea University kindly conveyed us a generous offer from De Gruyter for us to prepare a second edition of the book. We are very grateful to them.Dirichlet forms
Basic theory of Dirichlet forms
Potential theory for Dirichlet forms
The scope of Dirichlet forms
Symmetric Markov processes
Analysis by symmetric Hunt processes
Stochastic analysis by additive functionals
Transformations of forms and processes