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Dirichlet Forms and Symmetric Markov Processes / Edition 2

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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 some new sections as well as several exercises with solutions. The book addresses to researchers and graduate students who wish to comprehend the area of Dirichlet forms and symmetric Markov processes.

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Editorial Reviews

Introduces the theory of symmetric Dirichlet forms, an axiomatic extension of the classical Dirichlet integrals in the direction of Markovian semigroups; unifies the theory with the probabilistic potential theory based on symmetric Markov processes; and develops it in conjunction with the stochastic analysis based on the additive functionals. For graduate and professional mathematicians and mathematical physicists with at least one course in functional analysis. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9783110218084
  • Publisher: De Gruyter, Walter, Inc.
  • Publication date: 12/13/2010
  • Series: De Gruyter Studies in Mathematics Series , #19
  • Edition description: Revised
  • Edition number: 2
  • Pages: 489
  • Product dimensions: 6.90 (w) x 9.60 (h) x 1.20 (d)

Meet the Author

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

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Table of Contents

Pt. I Dirichlet forms
Ch. 1 Basic theory of Dirichlet forms 3
Ch. 2 Potential theory for Dirichlet forms 64
Ch. 3 The scope of Dirichlet forms 98
Pt. II Symmetric Markov processes
Ch. 4 Analysis by symmetric Hunt processes 133
Ch. 5 Stochastic analysis by additive functionals 180
Ch. 6 Transformations of forms and processes 258
Ch. 7 Construction of symmetric Markov processes 292
App. A.1 Choquet capacities 308
App. A.2 An introduction to Hunt processes 310
App. A.3 A summary on martingale additive functionals 331
App. A.4 Regular representations of Dirichlet spaces 344
Notes 361
Bibliography 369
Index 389
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