On A Mixture Of Brenier and Strassen Theorems
Probability
2019-09-18 v2 Functional Analysis
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].
Keywords
Cite
@article{arxiv.1808.02681,
title = {On A Mixture Of Brenier and Strassen Theorems},
author = {Nathael Gozlan and Nicolas Juillet},
journal= {arXiv preprint arXiv:1808.02681},
year = {2019}
}