A conditional approach to the anticipating Girsanov transformation
We study the law of a stochastic differential equation \(d\xi_ t=d \omega_ t+k_ t (\xi,\omega)dt\), where the drift anticipates the future behavior of the Brownian path \(\omega\), 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 the first author [ibid. 90, No. 2, 223-240 (1991; Zbl 0735.60057)] leads to new versions of the anticipating Girsanov transformation of Ramer and Kusuoka, and in particular to explicit formulas for the Carleman-Fredholm determinant.
explicit formulas for the Carleman- Fredholm determinant
scientific article; zbMATH DE number 569045
scientific article