Mean rates of convergence of empirical measures in the Wasserstein metric
Mean rates of convergence of empirical measures in the Wasserstein metric
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Wasserstein 度量中经验测量的平均收敛率
DOI：
10.1016/0377-0427(94)90033-7
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发表时间：
1994
影响因子：
2.4
通讯作者：
R. Karandikar
中科院分区：
文献类型：
--
作者：
J. Horowitz;R. Karandikar
给出了序列独立同分布的经验测度之间的均方Wasserstein距离的上界。随机向量和序列的公共概率律。同样的结果也适用于无限可交换序列及其定向测度。同样，对于i.i.d.序列的随机过程，上界获得的最大值的均方，超过0 t T，Wasserstein距离之间的经验措施的序列在和共同的边际法att。这些上界是在弱假设下得出的，并且与独立同分布的已知收敛速度相差不远。单位立方体上的均匀随机向量序列。然而，我们的方法，使我们能够得到任意分布的时刻条件下的结果，也给出了结果的过程。一个应用程序是所谓的扩散跳跃。这些过程的矩估计推导出可能是独立的利益。
An upper bound is given for the mean square Wasserstein distance between the empirical measure of a sequence of i.i.d. random vectors and the common probability law of the sequence. The same result holds for an infinite exchangeable sequence and its directing measure. Similarly, for an i.i.d. sequence of stochastic processes, an upper bound is obtained for the mean square of the maximum, over 0 ⩽t⩽T, of the Wasserstein distance between the empirical measure of the sequence at timetand the common marginal law att. These upper bounds are derived under weak assumptions and are not very far from the known rate of convergence pertaining to an i.i.d. sequence of uniform random vectors on the unit cube. Our approach, however, allows us to get results for arbitrary distributions under moment conditions and also gives results for processes. An application is given to so-called diffusions with jumps. Moment estimates for these processes are derived which may be of independent interest.