Journal of Applied Mathematics and Stochastic Analysis
Volume 7 (1994), Issue 3, Pages 239-246
On transformations of Wiener space
1Ukranian Academy of Science, Institute of Mathematics, Kiev, Ukraine
2Michigan State University, Department of Mathematics, East Lansing 48824, MI, USA
Received 1 February 1994; Revised 1 April 1994
Copyright © 1994 Anatoli V. Skorokhod. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.