Local times of self-intersection and sample path properties of Volterra Gaussian processes

Abstract

We study a Volterra Gaussian process of the form $X(t)={\int }_0^{t}K(t,s)dW(s),$ where $W$ is a Wiener process and $K$ is a continuous kernel. In dimension one, we prove a law of the iterated logarithm, discuss the existence of local times and verify a continuous dependence between the local time and the kernel that generates the process. Furthermore, we prove the existence of the Rosen renormalized self-intersection local times for a planar Gaussian Volterra process.

25 pages, no figures