Applications of the degree theorem to absolute continuity on Wiener space
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 \[ \Lambda_ F=\text{det}_ 2 (1+\nabla F) \text{Exp} \{-\delta F- \textstyle{{1 \over 2}} | F |^ 2\}. \]
scientific article; zbMATH DE number 569075