Unicité de solutions d'équations différentielles sur l'espace de Wiener
This is a natural continuation of the author's work [ibid. 54, 206-227 (1983; Zbl 0524.47028)]. Differential calculus in the sense of Malliavin is taken on the Wiener space X. The equations considered are of the type: \(du/dt=A(u(t)),\quad u(0)=x\in X,\) where A is defined on X with values in the Cameron-Martin subspace and is supposed to belong to certain Sobolev classes with respect to Wiener measure \(\mu\). Then a result of uniqueness of solutions (\(\mu\)-a.e.) is proved with the aid of a change of variables formula under the action of the flow.
Differential calculus in the sense of Malliavin
Sobolev classes with respect to Wiener measure
scientific article; zbMATH DE number 3877843