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

TL;DR

This paper investigates the regularity of resolvent operators for time-changed Brownian motions, establishing local Hölder continuity under specific conditions and providing bounds for the Hölder exponent.

Contribution

It introduces new Hölder estimates for resolvents of time-changed Brownian motions under Revuz measure regularity conditions.

Findings

Resolvents are locally Hölder continuous in space.

Lower bounds for the Hölder continuity exponent are derived.

Results depend on regularity conditions of associated measures.

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.