布朗鞅Monge迁移问题的一个解
A solution to the Monge transport problem for Brownian martingales
摘要：
我们提供了一个解决方案的问题，最优输运布朗鞅在一般尺寸的运输成本满足一定的次谐波性质的目标变量，以及随机版本的标准“扭曲条件”经常使用的确定性蒙赫运输理论。该设置尤其包括距离成本$c(x,y)=|x-y|$的情况。我们证明了解的存在性和唯一性，并将其描述为布朗运动第一次遇到由相应对偶问题的解所确定的障碍。
英文摘要：
We provide a solution to the problem of optimal transport by Brownian martingales in general dimensions whenever the transport cost satisfies certain subharmonic properties in the target variable, as well as a stochastic version of the standard "twist condition" frequently used in deterministic Monge transport theory. This setting includes in particular the case of the distance cost $c(x,y)=|x-y|$. We prove existence and uniqueness of the solution and characterize it as the first time Brownian motion hits a barrier that is determined by solutions to a corresponding dual problem.
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