Unrenormalized intersection local time of Brownian motion and its local time representation

Abstract

We consider the intersection local time of Brownian motion without renormalization through Itô-Wiener expansions. In order to recognize the existence, we extend the Watanabe space. We also discuss how to substitute Wiener functionals for parameters of a generalized Wiener functional. As a consequence a relationship between the unrenormalized intersection local time and the local time is clarified.