Preface
Notation
Part I. Dirichlet forms
Chapter 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
Chapter 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
Chapter 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
Part II. Symmetric Markov processes
Chapter 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
Chapter 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
Chapter 6. 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
6.3. Transformations by supermartingale multiplicative functionals
Chapter 7. Construction of symmetric Markov processes
7.1. Construction of a Markovian transition function
7.2. Construction of a symmetric Hunt process
7.3. Dirichlet forms and Hunt processes on a Lusin space
A 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
Notes
Bibliography
Index