Summary
LetT(ω)=ω+F(ω) be a transformation from the Wiener space to itself with the range ofF(ω) assumed to be in the Cameron-Martin space. The absolute continuity and the density function associated withT is considered;T is assumed to be embedded in or defined through a parameterizationT t ω=ω+F t (ω) andF t is assumed to be differentiable int. The paper deals first with the case where the range of thet-derivative ofF t (ω) is also in the Cameron-Martin space and new representations for the Radon-Nikodym derivative and the Carleman-Fredholm determinant are derived. The case where thet-derivative ofF t is not in the Cameron-Martin space is considered next and results on the absolute continuity and the density function, under conditions which are considerably weaker than previously known conditions, are presented.
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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. Transformation of Wiener measure under anticipative flows. Probab. Th. Rel. Fields 93, 91–136 (1992). https://doi.org/10.1007/BF01195390
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DOI: https://doi.org/10.1007/BF01195390