Local Times for Superdiffusions

Abstract

In this work we study local times for a class of measure-valued Markov processes known as superprocesses. We begin by deriving analogues of well-known properties of ordinary local times. Then, restricting our attention to a class of superprocesses (which includes the important case of super-Brownian motion), we prove more detailed properties of the local times, such as joint continuity and a global Holder condition. These are then used to obtain path properties of the superprocesses themselves. For example, we compute the Hausdorff dimension of the "level sets" of super-Brownian motion.