Construction of some processes on the Wiener space associated to second order operators (Q2718434)

A process \(\xi\) on the Wiener space \(X\) is called tangent process if it is an \(R^{d}\)-valued semimartingale with Itô differential \( d_{\tau}\xi_{\alpha}=a_{\alpha}^{\beta} dx_{\beta}(\tau)+b_{\alpha} d\tau\), where \(\alpha,\beta=1,\ldots,d\), \(a_{\alpha}^{\beta}=-a^{\alpha}_{\beta}\), \(a_{\alpha}^{\beta}(0)=0\), and such that \(\xi\) can also be represented in terms of a Stratonovic integral. The author proves that it is possible to associate a diffusion process to second-order perturbations of the Ornstein-Uhlenbeck operator \(L\) on the Wiener space of the form \(\frac{1}{2} \sum_{k}{\mathcal L}^{2}_{\xi_{k}}\) with \(\xi_{k}\) tangent processes.