Nonlinear Transformations on the Wiener Space
Nonlinear Transformations on the Wiener Space
We study shift transformations on a general abstract Wiener space $(E, H, \mu)$, which have the form: $E \ni \omega \mapsto \mathscr{J}^\phi\omega \equiv \omega - \int^T_0 \phi_t(\omega)Z(dt) \in E,$ where $\phi_t(\omega)$ is a scalar function on $\lbrack 0, T\rbrack \times E$ and $Z$ is an orthogonal $H$-valued measure. Under suitable …