A quasi-sure flow property and the equivalence of capacities for differential equations on the Wiener Space
type: Item
instance of: scholarly article
title: A quasi-sure flow property and the equivalence of capacities for differential equations on the Wiener Space
zbMATH Open document ID: 0879.47028
author: Yon Sik Yun
published in: Journal of Functional Analysis
publication date: 1996-06-30T00:00:00Z
review text: The author considers the problem \[ d/dt \bigl(U_t (x)\bigr) =A\bigl(U_t(x) \bigr), \quad U_0(x) =x, \tag{1} \] in an abstract Wiener space \((X,H,\mu)\) in which \(A\) is a vector field on \(X\), \(A:X\to H\), \(A\) is smooth in the sense of Malliavin. In an earlier paper the author constructed a solution \(U_t(x)\) of (1) which satisfies the equation quasi-everywhere i.e. except of a ``slim set''. The considered paper deals with refinements of the earlier results. Especially that the mapping \(x\to U_t(x)\) preserves the condition \[ U_t\circ U_s(x) =U_{t+s} (x). \]
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 880569
zbMATH Keywords: differential equation in the Malliavin sense
zbMATH Keywords: equivalence of capacities
zbMATH Keywords: slim set
zbMATH Keywords: abstract Wiener space
zbMATH Keywords: vector field
reviewed by: Tadeusz Dłotko
MaRDI profile type: Publication
full work available at URL: jfan.1996.0051
OpenAlex ID: W1989963505
DOI: 10.1006/JFAN.1996.0051
description: scientific article; zbMATH DE number 880569