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On A Mixture Of Brenier and Strassen Theorems (1808.02681v2)
Published 8 Aug 2018 in math.PR and math.FA
Abstract: We give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in [33]. Optimal plans are composition of a deterministic transport given by the gradient of a continuously differentiable convex function followed by a martingale coupling. We also establish some connections with Caffarelli's contraction theorem [14].
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