论文标题
向后的Martingale运输和Fitzpatrick在伪 - 欧几里得空间中的功能
Backward martingale transport and Fitzpatrick functions in pseudo-Euclidean spaces
论文作者
论文摘要
我们在伪欧国人太空$ s $中研究了最佳的运输问题，并在倒数欧克利达人的倒数限制中进行了落后的限制。我们表明，双重问题包括最小化与最大$ S $单酮集相关的Fitzpatrick函数的预期值。最佳计划$γ$和最佳的最大$ S $ SONONONE SET $ G $的特征是$ g $的$ S $ -Frocojection的支持包含$γ$的支持。对于高斯随机变量$ y $，我们会得到独特的分解：$ y = x+z $，其中$ x $和$ z $分别是独立的高斯随机变量，分别采用$ s $空间的互补正线性和负线性子空间。
We study an optimal transport problem with a backward martingale constraint in a pseudo-Euclidean space $S$. We show that the dual problem consists in the minimization of the expected values of the Fitzpatrick functions associated with maximal $S$-monotone sets. An optimal plan $γ$ and an optimal maximal $S$-monotone set $G$ are characterized by the condition that the support of $γ$ is contained in the graph of the $S$-projection on $G$. For a Gaussian random variable $Y$, we get a unique decomposition: $Y = X+Z$, where $X$ and $Z$ are independent Gaussian random variables taking values, respectively, in complementary positive and negative linear subspaces of the $S$-space.
