A WHITE NOISE APPROACH TO THE SELF-INTERSECTION LOCAL TIMES OF A GAUSSIAN PROCESS

Abstract

In this paper we show that for any spatial dimension the renormalized self-intersection local times of a certain Gaussian process defined by indefinite Wiener integral exist as Hida distributions. An explicit expression for the chaos decomposition in terms of Wick tensor powers of white noise is also obtained. We also study a regularization of the self-intersection local times and prove a convergence result in the space of Hida distributions.

DOI : http://dx.doi.org/10.22342/jims.20.2.136.111-124