Description
Thisbook deals with analytic treatments of Markov processes. Symmetric Dirichlet forms andtheir associated Markov processes are important and powerful toolsin the theory of Markovprocesses and their applications. The theoryis well studied and used in various fields. In this monograph, we intend togeneralize the theory to non-symmetric and time dependent semi-Dirichlet forms. By this generalization, we can cover the wide class of Markov processes and analytic theory which do not possess the dualMarkov processes. In particular, under the semi-Dirichlet form setting, the stochastic calculus is not well established yet.In this monograph, we intend to give an introduction to such calculus. Furthermore, basic examples different from the symmetric cases are given.Thetext is writtenfor graduate students, but alsoresearchers. Y. Oshima, Kumamoto University, Japan. 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
