Entrance law, exit system and lévy system of time changed processes

Let (X, X̂) be a pair of Borel standard processes on a Lusin space E that are in weak duality with respect to some σ-finite measure m that has full support on E. Let F be a finely closed subset of E. In this paper, we obtain the characterization of a Lévy system of the time changed process of X by a positive continuous additive functional (PCAF in abbreviation) of X having support F, under the assumption that every m-semipolar set of X is m-polar for X. The characterization of the Lévy system is in terms of Feller measures, which are intrinsic quantities for the part process of X killed upon leaving E \ F. Along the way, various relations between the entrance law, exit system, Feller measures and the distribution of the starting and ending point of excursions of X away from F are studied. We also show that the time changed process of X is a special standard process having a weak dual and that the μ-semipolar set of Y is μ-polar for Y, where μ is the Revuz measure for the PCAF used in the time change.