On transformations of Wiener space

The authors consider transformations of the form on the space C of all continuous functions , where is a measurable function which is -measurable for a fixed s and is the σ -algebra generated by . It is supposed that maps the Wiener measure on into a measure which is equivalent with respect to . The authors study some conditions of invertibility of such transformations. They also consider stochastic differential equations of the form where is a Wiener process. The authors prove that this equation has a unique strong solution if and only if it has a unique weak solution.