The Monge problem in Wiener Space

TL;DR

This paper investigates the Monge optimal transport problem within infinite-dimensional Wiener spaces, establishing existence results under conditions where both measures are absolutely continuous with respect to the Gaussian measure.

Contribution

It provides the first existence theorem for the Monge problem in Wiener space with absolutely continuous marginals.

Findings

Existence of solutions under absolute continuity conditions

Extension of optimal transport theory to infinite-dimensional Gaussian spaces

Framework applicable to stochastic analysis and probability theory

Abstract

We address the Monge problem in the abstract Wiener space and we give an existence result provided both marginal measures are absolutely continuous with respect to the infinite dimensional Gaussian measure {\gamma}.