Applications of the degree theorem to absolute continuity on Wiener space. (English) Zbl 0794.60033
Let \((\Omega,H,P)\) be an abstract Wiener space and define a shift on \(\Omega\) by \(T(\omega)=\omega+F(\omega)\) where \(F\) is an \(H\)-valued random variable. We study the absolute continuity of the measures \(P \circ T^{-1}\) and \((\Lambda_ FP) \circ T^{-1}\) with respect to \(P\) by using the techniques of the degree theory of Wiener maps, where
\[
\Lambda_ F=\text{det}_ 2 (1+\nabla F) \text{Exp} \{-\delta F- \textstyle{{1 \over 2}} | F |^ 2\}.
\]
Reviewer: A.S.Üstünel
MSC:
| 60G30 | Continuity and singularity of induced measures |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
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