The composition of Wiener functionals with non absolutely continuous Shifts |
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Authors: | A. S. Üstünel M. Zakai |
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Affiliation: | (1) E.N.S.T., 46, rue Barrault, F-75634 Paris, France;(2) Department of Electrical Engineering, Technion, 32000 Haifa, Israel |
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Abstract: | Summary In this paper we study some classes of Wiener functionals whose elements can be composed with a non-linear, non-absolutely continous transformation of the form of perturbation of identity in the direction of Cameron-Martin space. We show that under certain conditions the image of the Wiener measure under the above transformation induces a generalized Wiener functional on certain Sobolev spaces generalizing the Radon-Nikodym relation to non absolutely continuous transformations. A series representation for the generalized Radon-Nikodym derivative is presented and conditional expectations of some generalized random variables are considered. |
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Keywords: | 60H05 60G15 60G30 46G05 46G12 58B10 |
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