Moduli of continuity of local times of strongly symmetric Markov processes via Gaussian processes

Abstract

LetX be a strongly symmetric standard Markov process on a locally compact metric spaceS with 1-potential densityu 1(x, y). Let {L t y , (t, y)∈R +×S} denote the local times ofX and letG={G(y), y∈S} be a mean zero Gaussian process with covarianceu 1(x, y). In this paper results about the moduli of continuity ofG are carried over to give similar moduli of continuity results aboutL t y considered as a function ofy. Several examples are given with particular attention paid to symmetric Levy processes.