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Potential Theory and Right Processes

Bibliographic Details
Main Authors: Beznea, Lucian, Boboc, Nicu (Author)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 2004, 2004
Edition:1st ed. 2004
Series:Mathematics and Its Applications
Subjects:
Mathematical And Computational Biology
Probability Theory
Biomathematics
Potential Theory (mathematics)
Applications Of Mathematics
Mathematics
Potential Theory
Probabilities
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

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