Potential Theory and Right Processes
Main Authors: | , |
---|---|
Format: | eBook |
Language: | English |
Published: |
Dordrecht
Springer Netherlands
2004, 2004
|
Edition: | 1st ed. 2004 |
Series: | Mathematics and Its Applications
|
Subjects: | |
Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Excessive Functions
- 1.1 Sub-Markovian resolvent of kernels
- 1.2 Basics on excessive functions
- 1.3 Fine topology
- 1.4 Excessive measures
- 1.5 Ray topology and compactification
- 1.6 The reduction operation and the associated capacities
- 1.7 Polar and semipolar sets. Nearly measurable functions
- 1.8 Probabilistic interpretations: Sub-Markovian resolvents and right processes
- 2 Cones of Potentials and H-Cones
- 2.1 Basics on cones of potentials and H-cones
- 2.2 ?-Balayages on cones of potentials
- 2.3 Balayages on H-cones
- 2.4 Quasi bounded, subtractive and regular elements of a cone of potentials
- 3 Fine Potential Theoretical Techniques
- 3.1 Cones of potentials associated with a sub-Markovian resolvent
- 3.2 Regular excessive functions, fine carrier and semipolarity
- 3.3 Representation of balayages on excessive measures
- 3.4 Quasi bounded, regular and subtractive excessive measures
- 3.5 Tightness for sub-Markovian resolvents
- 7.4 Subordinate resolvents in weak duality
- 7.5 Semi-Dirichlet forms
- 7.6 Weak duality induced by a semi-Dirichlet form
- 7.7 Probabilistic interpretations: Multiplicative functionals in weak duality
- A Appendix
- A.1 Complements on measure theory, kernels, Choquet boundary and capacity
- A.2 Complements on right processes
- A.4 Basics on coercive closed bilinear forms
- Notes
- 3.6 Localization in excessive functions and excessive measures
- 3.7 Probabilistic interpretations: Continuous additive functionals and standardness
- 4 Strongly Supermedian Functions and Kernels
- 4.1 Supermedian functionals
- 4.2 Supermedian ?-quasi kernels
- 4.3 Strongly supermedian functions
- 4.4 Fine densities
- 4.5 Probabilistic interpretations: Homogeneous random measures
- 5 Subordinate Resolvents
- 5.1 Weak subordination operators
- 5.2 Inverse subordination
- 5.3 Probabilistic interpretations: Multiplicative functionals
- 6 Revuz Correspondence
- 6.1 Revuz measures
- 6.2 Hypothesis (B) of Hunt
- 6.3 Smooth measures and sub-Markovian resolvents
- 6.4 Measure perturbation of sub-Markovian resolvents
- 6.5 Probabilistic interpretations: Positive left additive functionals
- 7 Resolvents under Weak Duality Hypothesis
- 7.1Weak duality hypothesis
- 7.2 Natural potential kernels and the Revuz correspondence
- 7.3 Smooth and cosmooth measures