论文标题
Strassen定理和Choquet理论在最佳传输问题上的应用，均匀凸出功能和均匀平滑函数
Applications of Strassen's theorem and Choquet theory to optimal transport problems, to uniformly convex functions and to uniformly smooth functions
论文作者
论文摘要
我们提供了对各种最佳传输问题的统一解释，因为在给定的一对概率度量的所有Choquet表示方面，线性函数的最小化，相对于某个函数凸锥有序。这使我们能够提供二元公式的新颖证明。我们的工具包括Strassen的定理。 我们提供了原始问题和双重问题的新公式，用于使用欧几里得空间上凸的概率衡量标准的一组新颖的概率测量值的新颖表示。我们表现出与均匀凸出和均匀平滑函数的链接，并提供了此类功能的新表征。 我们介绍了Martingale三角不平等的概念。我们表明，Kantorovich-Rubinstein二重性在Martingale环境中具有类比，采用满足不平等的成本功能。
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.
