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Preprints, Working Papers, ... Year : 2022

WEAK OPTIMAL TRANSPORT WITH UNNORMALIZED KERNELS

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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Dates and versions

hal-03623104 , version 1 (29-03-2022)
hal-03623104 , version 2 (26-10-2023)

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Philippe Choné, Nathael Gozlan, Francis Kramarz. WEAK OPTIMAL TRANSPORT WITH UNNORMALIZED KERNELS. 2022. ⟨hal-03623104v2⟩
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