Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593045 | Journal of Functional Analysis | 2006 | 27 Pages |
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.
Related Topics
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