, Volume 95, Issue 4, pp 509-520

Applications of the degree theorem to absolute continuity on Wiener space

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Summary

Let (Ω,H, P) be an abstract Wiener space and define a shift on Ω byT(ω)=ω+F(ω) whereF is anH-valued random variable. We study the absolute continuity of the measuresPºT −1and (Λ F PT ∔1 with respect toP using the techniques of the degree theory of Wiener maps, where Λ F =det2(1+▽F) × Exp{−δF−1/2|F|2}.