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 P)ºT ∔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}.
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The work of the second author was supported by the fund for promotion of research at the Technion
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Üstünel, A.S., Zakai, M. Applications of the degree theorem to absolute continuity on Wiener space. Probab. Th. Rel. Fields 95, 509–520 (1993). https://doi.org/10.1007/BF01196731
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DOI: https://doi.org/10.1007/BF01196731