Energy decomposition by potential level

Abstract

In the first part we study excessive functions for a Markov process that are continuous semimartingales along the sample paths. The property then follows from the theory of local times of semimartingales. We next treat the case of Dirichlet spaces and show that, if u is a quasi-continuous version of a function u belonging to a regular Dirichlet space, then the image under u of the local energy measure of u is absolutely continuous with respect to Lebesgue measure. Finally, in a third part, we establish the occupation-time density property for certain Dirichlet processes.