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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

Citations:

Zbl 0735.60057
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References:

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