On flows associated to Sobolev vector fields in Wiener spaces: an approach \`a la DiPerna-Lions

TL;DR

This paper extends the DiPerna-Lions theory for ODEs with Sobolev vector fields to the setting of abstract Wiener spaces, broadening the theoretical framework for stochastic analysis.

Contribution

It introduces a novel approach to analyze flows associated with Sobolev vector fields in infinite-dimensional Wiener spaces, adapting DiPerna-Lions theory to this context.

Findings

Established existence and uniqueness of flows in Wiener spaces

Extended DiPerna-Lions theory to infinite-dimensional setting

Provided new tools for stochastic differential equations

Abstract

In this paper we extend the DiPerna-Lions theory on ODEs with Sobolev vector fields to the setting of abstract Wiener spaces.