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arXiv · 1808.02681

On A Mixture Of Brenier and Strassen Theorems

Nathael Gozlan·Nicolas Juillet
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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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Nathael Gozlan, Nicolas Juillet. 2018-08-08. On A Mixture Of Brenier and Strassen Theorems. https://doi.org/10.1112/plms.12302

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