论文标题
Martingale Wasserstein不平等，以概率措施按凸顺序进行
Martingale Wasserstein inequality for probability measures in the convex order
论文作者
论文摘要
作者表明，凸订单中的两个一维概率度量承认，$ \ vert x-y \ vert $的积分小于其$ \ Mathcal w_1 $ distance（WasserSteantance（WasserStein距离）（wastex tance and Index $ 1 $ $ 1 $），这是一个符合的Martingale耦合。我们表明，用$ \ vert x-y \ vert^ρ$和$ \ MathcalW_ρ^ρ$替换$ \ vert x-y \ vert $和$ \ mathcal w_1 $，并不会导致有限的乘数常数。我们在这里表明，用$ \ MATHCALW_ρ$ times的产品替换$ \ MathcalW_ρ^ρ$时，将恢复有限常数。然后，我们研究了这种新的稳定性不等式对更高维度的概括。
It was shown by the authors that two one-dimensional probability measures in the convex order admit a martingale coupling with respect to which the integral of $\vert x-y\vert$ is smaller than twice their $\mathcal W_1$-distance (Wasserstein distance with index $1$). We showed that replacing $\vert x-y\vert$ and $\mathcal W_1$ respectively with $\vert x-y\vert^ρ$ and $\mathcal W_ρ^ρ$ does not lead to a finite multiplicative constant. We show here that a finite constant is recovered when replacing $\mathcal W_ρ^ρ$ with the product of $\mathcal W_ρ$ times the centred $ρ$-th moment of the second marginal to the power $ρ-1$. Then we study the generalisation of this new stability inequality to higher dimension.
