On A Mixture Of Brenier and Strassen Theorems

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].

References in corpus (6)

• On a problem of optimal transport under marginal martingale constraints
• Limits Of One Dimensional Diffusions
• Optimal martingale transport between radially symmetric marginals in general dimensions
• Local structure of multi-dimensional martingale optimal transport
• A Theory of Transfers: Duality and convolution
• From Hopf-Lax formula to optimal weak transfer plan

Cited by in corpus (4)

• Transport-majorization to analytic and geometric inequalities
• Shadow martingales -- a stochastic mass transport approach to the peacock problem
• On the equivalence of static and dynamic weak optimal transport
• On Strassen's Theorem for support functions