Potential Theory and Right Processes

Introduction. 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. sigma-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 lambda-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 (i) 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.