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arXiv · 2203.16227

Weak optimal transport with unnormalized kernels

Philippe Choné·Nathael Gozlan·Francis Kramarz
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Abstract

We introduce a new variant of the weak optimal transport problem where mass is distributed from one space to the other through unnormalized kernels. We give sufficient conditions for primal attainment and prove a dual formula for this transport problem. We also obtain dual attainment conditions for some specific cost functions. As a byproduct we obtain a transport characterization of the stochastic order defined by convex positively 1-homogenous functions, in the spirit of Strassen theorem for convex domination.

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Philippe Choné, Nathael Gozlan, Francis Kramarz. 2022-03-30. Weak optimal transport with unnormalized kernels. https://arxiv.org/abs/2203.16227

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