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《狄氏型和對稱瑪律科夫過程》是學習狄氏型和對稱瑪律科夫過程的標準參考書。第一部分主要包括對狄氏型理論的介紹和綜合理解。狄氏型是在瑪律科夫半群方向下的一種經典的狄氏積分的公理化擴張。第二部分包括分析理論，對稱瑪律科夫理論的概率位勢理論，以及加性泛函數等。本書各章有習題，書後附有題解。讀者對象：應用數學領域的研究人員和研究生。
本書由3位日本數學家共同撰寫，分別是Masatoshi Fukushima, Yoichi Oshima, Masayoshi Takeda。
Preface to the first and second edition
Notation
Ⅰ Dirichlet Forms
1 Basic theory of Dirichlet forms
1.1 Basic notions
1.2 Examples
1.3 Closed forms and semigroups
1.4 Dirichlet forms and Markovian semigroups
1.5 Transience of Dirichlet spaces and extended Dirichlet spaces
1.6 Global properties of Markovian semigroups
2 Potential theory for Dirichlet forms
2.1 Capacity and quasi continuity
2.2 Measures of finite energy integrals
2.3 Reduced functions and spectral synthesis
2.4 Capacities and Sobolev type inequalities
3 The scope of Dirichlet forms
3.1 Closability and the smallest closed extensions
3.2 Formulae of Beurling—Deny and LeJan
3.3 Maximum Markovian extensions
Ⅱ Symmetric Markov processes
4 Analysis by symmetric Hunt processes
4.1 Smallness of sets and symmetry
4.2 Identification of potential theoretic notions
4.3 Orthogonal projections and hitting distributions
4.4 Parts of forms and processes
4.5 Continuity，killing，and jumps of sample paths
4.6 Quasi notions，fine notions and global properties
4.7 Irreducible recurrence and ergodicity
4.8 Recurrence and Poincar6 type inequalities
5 Stochastic analysis by additive functionals
5.1 Positive continuous additive functionals and smooth measures
5.2 Decomposition of additive functionals of finite energy
5.3 Martingale additive functionals and Beurling—Deny formulae
5.4 Continuous additive functionals of zero energy
5.5 Extensions to additive functionals locally of finite energy
5.6 Martingale additive functionals of finite energy and stochastic integrals
5.7 Forward and backward martingale additive functionals
Transformations of forms and processes
6.1 Perturbed Dirichlet forms and killing by additive functionals
6.2 Traces of Dirichlet forms and time changes by additive functionals
6.2.1 Transient case
6.2.2 General case
6.3 Transformations by supermartingale multiplicative functionals
6.4 Donsker—Varadhan type large deviation principle
Construction of symmetric Markov processes
7.1 Construction of a Markovian transition function
7.2 Construction of a symmetric Hunt process
Appendix
A.1 Choquet capacities
A.2 An introduction to Hunt processes
A.3 A summary on martingale additive functionals
A.4 Regular representations of Dirichlet spaces
A.5 Solutions to Exercises
Notes
Bibliography
Index
