Dirichlet Forms and Symmetric Markov Processes.
Dirichlet Forms and Symmetric Markov Processes (De Gruyter Studies in Mathematics).
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| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin :
De Gruyter,
1994
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| Series: | De Gruyter studies in mathematics.
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| Subjects: | |
| Local Note: | ProQuest Ebook Central |
Table of Contents:
- 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 LeJan3.3. 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 energy5.3. 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 functionalsChapter 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
