Parseval恒等式与最优输运映射
Parseval's Identity and Optimal Transport Maps
摘要：
最近的研究结果最优输运映射之间的分布函数共享相同的copula表明，组件的解决方案是最优的映射之间的边缘分布。这是一个重要的发现，因为在多元设置最佳的地图是很难找到的，只有在少数特殊情况下已知。在本文中，我们推广的结果共同copula共享一个共同的copula变量的正交变换也有一个已知的最佳映射。我们通过建立一类正态分布的尺度混合的成员之间的最优映射来说明这一点。
英文摘要：
Recent findings for optimal transport maps between distribution functions sharing the same copula show that componentwise the solution is the optimal map between marginal distributions. This is an important discovery since in the multivariate setting optimal maps are difficult to find and only known in a few special cases. In this paper, we extend the result on common copulas by showing that orthonormal transformations of variables sharing a common copula also have a known optimal map. We illustrate this by establishing optimal maps between members of a class of scale mixture of normal distributions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
