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
收藏
页码：6039 / 6092
页数：54
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