H\"{o}lder estimates for resolvents of time-changed Brownian motions

Abstract

This paper studies time changes of Brownian motions by positive continuous additive functionals. Under a certain regularity condition on the associated Revuz measures, we prove that the resolvents of the time-changed Brownian motions are locally H\"{o}lder continuous in the spatial components. We also obtain lower bounds for the indice of the H\"{o}lder continuity.