Solution of the Monge-Ampère equation on Wiener space for general log-concave measures |
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Authors: | D. Feyel |
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Affiliation: | a Université d’Evry-Val-d’Essone, 91025 Evry Cedex, France b ENST, Dépt. Infres, 46, rue Barrault, 75634, Paris Cedex 13, France |
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Abstract: | In this work we prove that the unique 1-convex solution of the Monge-Kantorovitch measure transportation problem between the Wiener measure and a target measure which has an H-log-concave density, in the sense of Feyel and Üstünel [J. Funct. Anal. 176 (2000) 400-428], w.r.t the Wiener measure is also the strong solution of the Monge-Ampère equation in the frame of infinite-dimensional Fréchet spaces. We further enhance the polar factorization results of the mappings which transform a spread measure to another one in terms of the measure transportation of Monge-Kantorovitch and clarify the relation between this concept and the Itô-solutions of the Monge-Ampère equation. |
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Keywords: | Optimal mass transportation Monge-Ampè re equation Wiener space Itô calculus |
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