Dirichlet Forms and Symmetric Markov Processes

Masatoshi Fukushima; Yoichi Oshima; Masayoshi Takeda

Masatoshi Fukushima, Yoichi Oshima und Masayoshi Takeda

Dirichlet Forms and Symmetric Markov Processes

In: De Gruyter Studies in Mathematics, 19

De Gruyter | 2010

https://doi.org/10.1515/9783110218091

Übersicht
Inhalt

Über dieses Buch

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.

Autoreninformation

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

Rezensionen

"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

Frontmatter Erfordert eine Authentifizierung Zugänglich PDF	I
Preface to the first and second edition Erfordert eine Authentifizierung Zugänglich PDF	V
Preface to the second edition Erfordert eine Authentifizierung Zugänglich PDF	VI
Contents Erfordert eine Authentifizierung Zugänglich PDF	VII
Notation Erfordert eine Authentifizierung Zugänglich PDF	IX
Part I: Dirichlet Forms
Chapter 1: Basic theory of Dirichlet forms Erfordert eine Authentifizierung Zugänglich PDF	3
Chapter 2: Potential theory for Dirichlet forms Erfordert eine Authentifizierung Zugänglich PDF	66
Chapter 3: The scope of Dirichlet forms Erfordert eine Authentifizierung Zugänglich PDF	109
Part II: Symmetric Markov processes
Chapter 4: Analysis by symmetric Hunt processes Erfordert eine Authentifizierung Zugänglich PDF	151
Chapter 5: Stochastic analysis by additive functionals Erfordert eine Authentifizierung Zugänglich PDF	221
Chapter 6: Transformations of forms and processes Erfordert eine Authentifizierung Zugänglich PDF	307
Chapter 7: Construction of symmetric Markov processes Erfordert eine Authentifizierung Zugänglich PDF	369
Appendix Erfordert eine Authentifizierung Zugänglich PDF	382
Notes Erfordert eine Authentifizierung Zugänglich PDF	453
Bibliography Erfordert eine Authentifizierung Zugänglich PDF	461
Index Erfordert eine Authentifizierung Zugänglich PDF	485

(English)

Dirichlet Forms and Symmetric Markov Processes

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