AuthorBeznea, Lucian. author
TitlePotential Theory and Right Processes [electronic resource] / by Lucian Beznea, Nicu Boboc
ImprintDordrecht : Springer Netherlands : Imprint: Springer, 2004
Connect tohttp://dx.doi.org/10.1007/978-1-4020-2497-9
Descript VI, 370 p. online resource

CONTENT

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 -- 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 -- 7.1 Weak duality hypothesis -- 7.2 Natural potential kernels and the Revuz correspondence -- 7.3 Smooth and cosmooth measures -- 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


SUBJECT

  1. Mathematics
  2. Potential theory (Mathematics)
  3. Applied mathematics
  4. Engineering mathematics
  5. Probabilities
  6. Biomathematics
  7. Mathematics
  8. Potential Theory
  9. Probability Theory and Stochastic Processes
  10. Applications of Mathematics
  11. Mathematical and Computational Biology