Measure transport on Wiener space and the Girsanov theorem.
type: Item
instance of: scholarly article
title: Measure transport on Wiener space and the Girsanov theorem.
zbMATH Open document ID: 1036.60004
DOI: 10.1016/S1631-073X(02)02326-9
author: A. S. Üstünel
author: Denis Feyel
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2002-10-14T00:00:00Z
review text: Let \((W, H, \mu)\) be an abstract Wiener space. Assume that \(\nu_1, \nu_2\) are two probability measures on \((W, \mathcal{B}(W))\) absolutely continuous with respect to \(\mu.\) If the Wasserstein distance \(d_W(\nu_1, \nu_2)\) is finite, then it is proved that there exists a map \(T=I_W+\xi: W\to W\) such that \(\nu_2=T\nu_1,\) where \(\xi\) maps \(W\) into \(H\), is measurable and \(1\)-cyclically monotone. Moreover, \(T\) is invertible on the support of \(\nu_2\). Some applications of this result are given to the Monge-Ampere equation in infinite-dimensional spaces.
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 1777411
zbMATH Keywords: Abstract Wiener space
zbMATH Keywords: Wasserstein metric
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1777411