Markov Processes and Potential Theory
Markov Processes and Potential Theory
Academic Press
Published on 29. August 2011
312 pages
978-0-08-087341-1 (ISBN)
Description
Markov Processes and Potential Theory
More details
Persons
Content
- Front Cover
- Markov Processes and Potential Theory
- Copyright Page
- Contents
- Preface
- Chapter 0. Preliminaries
- 1. Notation
- 2. The Monotone Class Theorem
- 3. Topological Spaces
- Chapter I. Markov Processes
- 1. General Definitions
- 2. Transition Functions
- 3. General Definitions Continued
- 4. Equivalent Processes
- 5. The Measures Pµ
- 6. Stopping Times
- 7. Stopping Times for Markov Processes
- 8. The Strong Markov Property
- 9. Standard Processes
- 10. Measurability of Hitting Times
- 11. Further Properties of Hitting Times
- 12. Regular Step Processes
- Chapter ll. Excessive Functions
- 1. Introduction
- 2. Excessive Functions
- 3. Exceptional Sets
- 4. The Fine Topology
- 5. Alternative Characterization of Excessive Functions
- Chapter lll. Multiplicative Functionals and Subprocesses
- 1. Multiplicative Functionals
- 2. Subordinate Semigroups
- 3. Subprocesses
- 4. Resolvents and Strong Multiplicative Functionals
- 5. Excessive Functions
- 6. A Theorem of Hunt
- Chapter IV. Additive Functionals and Their Potentials
- 1. Additive Functionals
- 2. Potentials of Additive Functionals
- 3. Potentials of Continuous Additive Functionals
- 4. Potentials of Natural Additive Functionals
- 5. Classification of Excessive Functions
- Chapter V. Further Properties of Continuous Additive Functionals
- 1. Reference Measures
- 2. Continuous Additive Functionals
- 3. Fine Supports and Local Times
- 4. Balayage of Additive Functionals
- 5. Processes with Identical Hitting Distributions
- Chapter VI. Dual Processes and Potential Theory
- 1. Dual Processes
- 2. Potentials of Measures
- 3. Potentials of Additive Functionals
- 4. Capacity and Related Topics
- Notes and Comments
- Bibliography
- Index of Notation
- Subject Index
