论文标题
具有高斯输入的功能性中心极限定理中的收敛速度急剧
A Sharp Rate of Convergence in the Functional Central Limit Theorem with Gaussian Input
论文作者
论文摘要
当基础随机变量是高斯时，经典的中央限制定理（CLT）是微不足道的，但功能性CLT不是。本文的目的是研究连续函数空间中Wasserstein-1度量中固定高斯过程的功能性CLT。建立了匹配的上限和下边界，表明收敛速率稍快地比Lévy-Prokhorov指标中的速度快一些。
When the underlying random variables are Gaussian, the classical Central Limit Theorem (CLT) is trivial, but the functional CLT is not. The objective of the paper is to investigate the functional CLT for stationary Gaussian processes in the Wasserstein-1 metric on the space of continuous functions. Matching upper and lower bounds are established, indicating that the convergence rate is slightly faster than in the Lévy-Prokhorov metric.
