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This book contains original research papers by leading experts in
the fields of probability theory, stochastic analysis, potential
theory and mathematical physics. There is also a historical account
on Masatoshi Fukushima's contribution to mathematics, as well as
authoritative surveys on the state of the art in the field.
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
Poincare 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.
Masatoshi Fukushima is one of the most influential probabilists of
our times. His fundamental work on Dirichlet forms and Markov
processes made Hilbert space methods a tool in stochastic analysis
and by this he opened the way to several new developments. His
impact on a new generation of probabilists can hardly be
overstated. These Selecta collect 25 of Fukushima's seminal
articles published between 1967 and 2007.
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