Symmetric Markov processes, time change, and boundary theory /
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| Author / Creator: | Chen, Zhen-Qing. |
|---|---|
| Imprint: | Princeton : Princeton University Press, c2012. |
| Description: | xv, 479 p. ; 25 cm. |
| Language: | English |
| Series: | London Mathematical Society monographs ; vol. 35 London Mathematical Society monographs ; new ser., no. 35. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8552516 |
Table of 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. Symmeteic Hunt Processes and Rrgular 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 Functional of Symmetric Merkov 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 Symmetrix Markov Processes
- 5.1. Subprocesses and Perturbed Dirichlet Forms
- 5.2. Time Changes and Trace Dirichlet Forms
- 5.3. Examples
- 5.4. Energy Functional 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. Rrflected 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
