Chapter 4: Local Times in White Noise Analysis

In this chapter we give an overview of self intersection local times of Brownian motion paths and related processes in the framework of white noise analysis. More precisely, we show that self intersection local times are well defined Hida distributions as well as k-fold intersections. It turns out that the kernel functions of the chaos expansion are remarkably simple and exhibit clearly the dimension dependence. We use these kernel functions to study the regularity and convergence properties of self intersection local times.