Applications of Strassen's theorem and Choquet theory to optimal transport problems, to uniformly convex functions and to uniformly smooth functions☆

被引：1

作者：

Ciosmak, Krzysztof J. ^{[1
,2
]}

机构：

[1] Fields Inst Res Math Sci, 222 Coll St, Toronto, ON M5T 3J1, Canada

[2] Univ Toronto, Bahen Ctr, Dept Math, 40 St George St,Room 6290, Toronto, ON M5S 2E4, Canada

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2023年 / 232卷

基金：

英国工程与自然科学研究理事会;

关键词：

Strassen's theorem; Optimal transport; Uniform convexity; Kantorovich duality; GENERAL DUALITY THEOREM; MONGE SOLUTIONS; PROBABILITY;

D O I：

10.1016/j.na.2023.113267

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex cone of functions. This allows us to provide novel proofs of duality formulae. Among our tools is Strassen's theorem. We provide new formulations of the primal and the dual problem for martingale optimal transport employing a novel representation of the set of extreme points of probability measures in convex order on Euclidean space. We exhibit a link to uniformly convex and uniformly smooth functions and provide a new characterisation of such functions. We introduce a notion of martingale triangle inequality. We show that Kantorovich-Rubinstein duality bears an analogy in the martingale setting employing the cost functions that satisfy the inequality. (c) 2023 Elsevier Ltd. All rights reserved.

引用

页数：32

共 29 条

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