论文标题
Lipschitz在线上以凸顺序的瓦斯恒星预测的连续性
Lipschitz continuity of the Wasserstein projections in the convex order on the line
论文作者
论文摘要
在较弱的最佳运输框架内首先考虑了凸顺序中的Wasserstein投影，并在各种问题中发现了应用，例如浓度不平等和Martingale最佳运输。在维度一中，众所周知，具有给定平均值的概率度量集为晶格W.R.T.凸顺序。我们的主要结果是，与凸的最小和最大值相反，Wasserstein的投影是Lipschitz的连续性W.R.T. Wasserstein距离为1。此外，我们提供的例子显示了1-wasserstein距离获得的边界的清晰度。
Wasserstein projections in the convex order were first considered in the framework of weak optimal transport, and found application in various problems such as concentration inequalities and martingale optimal transport. In dimension one, it is well-known that the set of probability measures with a given mean is a lattice w.r.t. the convex order. Our main result is that, contrary to the minimum and maximum in the convex order, the Wasserstein projections are Lipschitz continuity w.r.t. the Wasserstein distance in dimension one. Moreover, we provide examples that show sharpness of the obtained bounds for the 1-Wasserstein distance.
