论文标题
非线性函数的经验措施的中心限制定理：超越IID设置
Central limit theorem over non-linear functionals of empirical measures: beyond the iid setting
论文作者
论文摘要
中心限制定理具有很大的规律，是概率理论中两个基本限制定理之一。 Benjamin Jourdain和Alvin TSE已扩展到独立和相同分布的随机向量的经验度量的非线性函数，该中心限制为线性函数众所周知。允许该延伸的主要工具是线性功能导数，这是最近开发的概率度量的Wasserstein空间上的派生概念之一。这项工作的目的是概括Jourdain和TSE所做的事情：为独立和非等级随机向量的非线性函数提供了一个中心限制定理，例如Ergodic Markov链的连续值。
The central limit theorem is, with the strong law of large numbers, one of the two fundamental limit theorems in probability theory. Benjamin Jourdain and Alvin Tse have extended to non-linear functionals of the empirical measure of independent and identically distributed random vectors the central limit theorem which is well known for linear functionals. The main tool permitting this extension is the linear functional derivative, one of the notions of derivation on the Wasserstein space of probability measures that have recently been developed. The purpose of this work is to generalize what has been done by Jourdain and Tse: provide a Central Limit Theorem for non-linear functionals of independent and non equidistributed random vectors such as the successive values of an ergodic Markov chain.
