| We begin by introducing Brownian motion, intersection local time, and symmetric stable processes. We then state some basic results concerning intersection local time and its derivative. The remainder of the thesis is devoted to the proofs of the main theorems, which pertain to the asymptotics of a family of integrals related to the intersection local times of Brownian motion and symmetric stable processes in R2. These integrals depend on a parameter epsilon, and we show that, upon dividing by a suitable function of epsilon, these integrals converge in law to a one dimensional Brownian motion as epsilon converges to 0. |
