## A conditional approach to the anticipating Girsanov transformation.(English)Zbl 0791.60038

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.
Reviewer: R.Buckdahn

### MSC:

 60H07 Stochastic calculus of variations and the Malliavin calculus 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60J65 Brownian motion 60J45 Probabilistic potential theory

Zbl 0735.60057
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### References:

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