Anatoli V. Skorokhod, "On transformations of Wiener space", International Journal of Stochastic Analysis, vol. 7, Article ID 584613, 8 pages, 1994. https://doi.org/10.1155/S1048953394000249
On transformations of Wiener space
We consider transformations of the form on the space of all continuous functions , , where is a measurable function which is -measurable for a fixed and is the -algebra generated by . It is supposed that maps the Wiener measure on into a measure which is equivalent with respect to . We study some conditions of invertibility of such transformations. We also consider stochastic differential equations of the form where is a Wiener process. We prove that this equation has a unique strong solution if and only if it has a unique weak solution.
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