The composition of Wiener functionals with non absolutely continuous shifts (Q1326277)

We study some classes of Wiener functionals whose elements can be composed with a nonlinear, non-absolutely continuous 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.