A conditional approach to the anticipating Girsanov transformation

Abstract

We study the law of a stochastic differential equation {Mathematical expression} where the drift anticipates the future behavior of the Brownian path ω, for example the endpoint. We first investigate anticipation of the endpoint, using a conditional Girsanov transformation and methods of Malliavin calculus. A combination with results of Buckdahn [2] leads to new versions of the anticipating Girsanov transformation of Ramer and Kusuoka, and in particular to explicit formulas for the Carleman-Fredholm determinant. © 1993 Springer-Verlag.