Representations for Continuous Additive Functionals of Super-Brownian and Super-Stable Processes

Stephen M. Krone


We study a class of continuous additive functionals for super-Brownian and super-stable processes. These are given in terms of a Tanaka-like formula that generalizes the one for local times. We give representations for these additive functionals in terms of the corresponding local times. As an example, we discuss fractional Laplacians of super-Brownian local times.