On Moduli of Continuity for Local Times of Fractional Stable Processes

Abstract

We establish estimates for moduli of continuity of the local times of a class of self-similar stable processes. Our arguments yield also sharp lower bounds for the Hausdorff measure of the level sets of these processes. Finally, we prove the continuity in law of the local times with respect to the self-similarity index for a wide class of self-similar stable processes.