Stein函数方法在弱相依随机变量中的应用
Stein's functional method for weakly dependent random variables
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中文总结 AI 辅助
本文扩展Stein函数方法，通过简化至有限维边际并采用块技术，为弱相依序列的Donsker不变原理建立了Wasserstein-1距离下的显式收敛速率。
中文摘要 AI 辅助
本文扩展了Stein函数方法，在弱相依条件下为Donsker不变原理建立了Wasserstein-1距离下的显式收敛速率。我们的方法首先将函数空间上分布间距离的界定问题简化为估计有限维边际分布间的距离。随后，我们采用Stein方法中标准的块技术来处理相依性。尽管我们的分析聚焦于φ-混合序列，但该方法可推广至其他满足适当协方差不等式的弱相依形式。
英文摘要
This article extends Stein's functional method to establish explicit rates of convergence in the Wasserstein-1 distance for Donsker's invariance principle under weak dependence. Our approach first reduces the problem of bounding distances between distributions on a function space to estimating distances between finite-dimensional marginals. We then employ the block technique, which is standard in Stein's methodology, to handle dependence. While our analysis focuses on $ϕ$-mixing sequences, the method extends to other forms of weak dependence admitting suitable covariance inequalities.
