标题： 平稳$α$-相关序列的样本分布与边缘分布之间的 Wasserstein 距离的行为 显示英文标题

标题： Behavior of the Wasserstein distance between the empirical and the marginal distributions of stationary $α$-dependent sequences

摘要： 我们研究经验分布与平稳$\alpha$-相关序列的边缘分布之间的1阶Wasserstein距离。 我们证明了对于任意p $\ge$ 1的p阶矩不等式，并给出了中心极限定理成立的一些条件。 我们将结果应用于区间上具有零点中性不动点的扩张映射的无界函数。 Wasserstein距离的矩不等式类似于部分和的著名von Bahr-Esseen或Rosenthal界，甚至在独立同分布随机变量的情况下似乎也是新的。 显示英文摘要

摘要： We study the Wasserstein distance of order 1 between the empirical distribution and the marginal distribution of stationary $\alpha$-dependent sequences. We prove some moments inequalities of order p for any p $\ge$ 1, and we give some conditions under which the central limit theorem holds. We apply our results to unbounded functions of expanding maps of the interval with a neutral fixed point at zero. The moment inequalities for the Wasserstein distance are similar to the well known von Bahr-Esseen or Rosenthal bounds for partial sums, and seem to be new even in the case of independent and identically distributed random variables.