Monge-Kantorovitch Measure Transportation and Monge-Ampère Equation on Wiener Space

By D. Feyel, A. Üstünel. 2004

168 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ea160502c0912878025658e0a374fad13bf29365

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Citations in the corpus

A User’s Guide to Optimal Transport (2013, unknown): “Üstünel ([36]).”
An introduction to sampling via measure transport (2016, background): “Generalizations of this result accounting for diﬀerent cost functions and spaces can be found in [19, 2, 27, 11].”
Gradient Flows: In Metric Spaces and in the Space of Probability Measures (2005, background): “10) an existence result in the case when X is a separable Hilbert space (compare with the result [67, 68] in Wiener spaces, where the cost function c(x, y) is finite only when x−y is in the Cameron-Martin space).”
On the sufficiency of c-cyclical monotonicity for optimality of transport plans (2008, background): “Detailed discussions about the c-cyclical monotonicity can be found for instance in [3, 7 , 8,11].”
On a mixture of Brenier and Strassen Theorems (2018, background): “This result has then been extended to various cost functions [26] and state spaces [4, 9, 21, 23, 24, 28, 29, 54] and has had numerous applications in PDE, geometric analysis or probability theory, see [3, 6, 72, 73] and the references therein.”
Existence and stability for Fokker–Planck equations with log-concave reference measure (2007, background): “This is one of the infinite-dimensional generalizations (see also [15] for another result in Wiener spaces) of the finite-dimensional result ensuring that whenever μ ∈ P2(R) is absolutely continuous with respect to L k, then there exists a unique optimal transport map that is also the gradient of a ”