Title

Occupation Times for Jump Processes

Date of Completion

January 2011

Keywords

Applied Mathematics|Mathematics

Degree

Ph.D.

Abstract

In this dissertation, we consider two different types of pure jump Markov processes. The first chapter is an introduction, in which we present some historical results pertaining to jump processes, and give motivation for our current work. In the second chapter, we prove that there is a lower bound on occupation times of sets by stable-like processes of order a. This result is then used to extend a Harnack inequality. The third chapter gives a proof of the support theorem for these processes, and show that we can approximate resolvents using smooth functions. In the fourth chapter of this dissertation, we consider a class of symmetric jump processes, and show that there is a lower bound on occupation times of sets. ^