Last Exit Times and Additive Functionals

Abstract

The various objects examined in this paper arise in the study of last exit times and balayage of additive functionals for standard Markov processes. The most important results concern the characterization of the Laplace transform of an entrance law, the relationship between the last exit distribution from a set and the capacity measure of the set, the characterization of projective sets and $d$-sets, and a last exit decomposition formula for finite sets $F$ which expresses the distribution of $X_t$ in terms of the last exit from $F$ prior to $t$.