WEAK OPTIMAL TRANSPORT WITH UNNORMALIZED KERNELS

被引：2

作者：

Chone, Philippe ^{[1
]}

Gozlan, Nathael ^{[2
]}

Kramarz, Francis ^{[3
,4
]}

机构：

[1] CREST, ENSAE, Inst Polytech Paris, Paris, France

[2] Univ Paris Cite, MAP5, CNRS, F-75006 Paris, France

[3] CREST, Inst Polytech Paris, ENSAE, Paris, France

[4] Uppsala Univ, Dept Econ, Uppsala, Sweden

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2023年 / 55卷 / 06期

基金：

欧洲研究理事会;

关键词：

optimal transport; weak optimal transport; duality; convex order; Strassen's theorem; PROBABILITY-MEASURES; REARRANGEMENT; COSTS;

D O I：

10.1137/22M1501301

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 the Strassen theorem for convex domination.

引用

页码：6039 / 6092

页数：54

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