Solution of the Monge-Ampere Equation on Wiener Space for log-concave measures

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dc.creatorFeyel, D.
dc.creatorUstunel, A. S.
dc.date2004-03-29
dc.date.accessioned2026-07-07T05:06:51Z
dc.date.available2026-07-07T05:06:51Z
dc.descriptionIn this work we prove that the unique 1-convex solution of the Monge problem contructed from the solution of the Monge-Kantorovitch problem between the Wiener measure and a target measure which has a log-concave density w.r.to the Wiener measure is also the strong solution of the Monge-Ampere equation in the frame of infinite dimensional Frechet spaces. We enhance also the polar factorization results of the mappings which transform a spread measure to another one of finite Wasserstein distance. Finally we calculate the semimartingale decomposition of the transport process with respect to its natural filtration and make the connection between the curved Brownian motion and the polar decomposition of the corresponding shifts.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/math/0403497
dc.identifierhttp://arxiv.org/abs/math/0403497
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70632
dc.subjectProbability
dc.subjectMathematical Physics
dc.subjectFunctional Analysis
dc.subject60H07, 60H05, 60H25, 60G15, 46G12, 47H05, 47H1, 35J60, 35B65, 35A30, 49Q20, 58E12, 26A16, 28C20
dc.titleSolution of the Monge-Ampere Equation on Wiener Space for log-concave measures
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