Semi-Dirichlet Forms and Markov Processes

Chapter 1 Dirichlet forms
1.1 Semi-Dirichlet forms and resolvents
1.2 Closability and regular Dirichlet forms
1.3 Transience and recurrence of Dirichlet forms
1.4 An auxiliary bilinear forms
1.5 Examples

Chapter 2 Some analytic properties of Dirichlet forms
2.1 Capacity
2.2 Qasi-continuity
2.3 Potential of measures
2.4 An orthogonal decomposition of Dirichlet forms

Chapter 3 Markov processes
3.1 Hunt processes
3.2 Excessive functions and negligible sets
3.3 Hunt processes associated with Dirichlet forms
3.4 Negligible sets of Hunt processes
3.5 Decomposition of Dirichlet forms

Chapter 4 Additive functionals and smooth measures
4.1 Positive continuous additive functionals
4.2 Dual PCAFs and duality measures
4.3 Time changes and killings by PCAFs

Chapter 5 Martingale AFs and AFs of zero energy
5.1 Decomposition of AFs
5.2 Beurling-Deny type decompositions
5.3 CAFs of zero energy
5.4 Martingale AFs of local Dirichlet forms
5.5 Transformations by multiplicative functionals
5.6 Conservativeness and recurrence of Dirichlet forms

Chapter 6 Time dependent Dirichlet forms
6.1 Time dependent Dirichlet forms and associated resolvents
6.2 Some parabolic potential theory
6.3 Associated space-time processes
6.4 Additive functionals and associated measures
6.5 Some stochastic calculus