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Index
Cover
Title
Copyright
Contents
Notation
Preface
Chapter 1. SYMMETRIC MARKOVIAN SEMIGROUPS AND DIRICHLET FORMS
1.1 Dirichlet Forms and Extended Dirichlet Spaces
1.2 Excessive Functions and Capacities
1.3 Quasi-Regular Dirichlet Forms
1.4 Quasi-Homeomorphism of Dirichlet Spaces
1.5 Symmetric Right Processes and Quasi-Regular Dirichlet Forms
Chapter 2. BASIC PROPERTIES AND EXAMPLES OF DIRICHLET FORMS
2.1 Transience, Recurrence, and Irreducibility
2.2 Basic Examples
2.3 Analytic Potential Theory for Regular Dirichlet Forms
2.4 Local Properties
Chapter 3. SYMMETRIC HUNT PROCESSES AND REGULAR DIRICHLET FORMS
3.1 Relations between Probabilistic and Analytic Concepts
3.2 Hitting Distributions and Projections I
3.3 Quasi Properties, Fine Properties, and Part Processes
3.4 Hitting Distributions and Projections II
3.5 Transience, Recurrence, and Path Behavior
Chapter 4. ADDITIVE FUNCTIONALS OF SYMMETRIC MARKOV PROCESSES
4.1 Positive Continuous Additive Functionals and Smooth Measures
4.2 Decompositions of Additive Functionals of Finite Energy
4.3 Probabilistic Derivation of Beurling-Deny Formula
Chapter 5. TIME CHANGES OF SYMMETRIC MARKOV PROCESSES
5.1 Subprocesses and Perturbed Dirichlet Forms
5.2 Time Changes and Trace Dirichlet Forms
5.3 Examples
5.4 Energy Functionals for Transient Processes
5.5 Trace Dirichlet Forms and Feller Measures
5.6 Characterization of Time-Changed Processes
5.7 Excursions, Exit System, and Feller Measures
5.8 More Examples
Chapter 6. REFLECTED DIRICHLET SPACES
6.1 Terminal Random Variables and Harmonic Functions
6.2 Reflected Dirichlet Spaces: Transient Case
6.3 Recurrent Case
6.4 Toward Quasi-Regular Cases
6.5 Examples
6.6 Silverstein Extensions
6.7 Equivalent Notions of Harmonicity
Chapter 7. BOUNDARY THEORY FOR SYMMETRIC MARKOV PROCESSES
7.1 Reflected Dirichlet Space for Part Processes
7.2 Douglas Integrals and Reflecting Extensions
7.3 Lateral Condition for L2-Generator
7.4 Countable Boundary
7.5 One-Point Extensions
7.6 Examples of One-Point Extensions
7.7 Many-Point Extensions
7.8 Examples of Many-Point Extensions
Appendix A. ESSENTIALS OF MARKOV PROCESSES
A.1 Markov Processes
A.2 Basic Properties of Borel Right Processes
A.3 Additive Functionals of Right Processes
A.4 Review of Symmetric Forms
Appendix B. SOLUTIONS TO EXERCISES
Notes
Bibliography
Catalogue of Some Useful Theorems
Index
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