Solution of the Monge-Ampère equation on Wiener space for general log-concave measures

DOI10.1016/j.jfa.2005.05.008zbMath1099.60042OpenAlexW2053725242MaRDI QIDQ2368784

Denis Feyel, Ali Süleyman Üstünel

Publication date: 28 April 2006

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2005.05.008

zbMATH Keywords

Gaussian measuresWiener spaceoptimal mass transportation\(H\)-log-concave densitiesÎto calculusItô-solutionMonge-Kan\-to\-ro\-vitch problem

Mathematics Subject Classification ID

Stochastic calculus of variations and the Malliavin calculus (60H07) Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds (46T12)

Related Items (9)

Kantorovich potentials and continuity of total cost for relativistic cost functions ⋮ Variational calculation of Laplace transforms via entropy on Wiener space and applications ⋮ Quantitative bounds on the rate of approach to equilibrium for some one-dimensional stochastic nonlinear Schrödinger equations ⋮ On the Kantorovich problem for nonlinear images of the Wiener measure ⋮ Sobolev estimates for optimal transport maps on Gaussian spaces ⋮ Some covariance inequalities in Wiener space ⋮ On the Monge and Kantorovich problems for distributions of diffusion processes ⋮ Optimal transport maps on infinite dimensional spaces ⋮ Regularity of the backward Monge potential and the Monge–Ampère equation on Wiener space

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