Unicité de solutions d'équations différentielles sur l'espace de Wiener
type: Item
instance of: scholarly article
title: Unicité de solutions d'équations différentielles sur l'espace de Wiener
zbMATH Open document ID: 0551.47019
DOI: 10.1016/0022-1236(84)90047-8
author: Ana Bela Cruzeiro
published in: Journal of Functional Analysis
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 3877843
zbMATH Keywords: differential equations on Wiener space
zbMATH Keywords: Differential calculus in the sense of Malliavin
zbMATH Keywords: Cameron-Martin subspace
zbMATH Keywords: Sobolev classes with respect to Wiener measure
zbMATH Keywords: change of variables formula
MaRDI profile type: Publication
full work available at URL: 0022-1236(84)90047-8
OpenAlex ID: W2040522266
cites work: Equations différentielles sur l'espace de Wiener et formules de Cameron- Martin non-linéaires
cites work: Q3336426
description: scientific article; zbMATH DE number 3877843