论文标题
浆果 - 与（几乎）尖锐的依赖条件结合
A Berry-Esseen bound with (almost) sharp dependence conditions
论文作者
论文摘要
假设固定序列的（归一化）部分总和会收敛到标准的正常随机变量。给出足够的时刻，什么时候我们在统一度量中有$ n^{ - 1/2} $的收敛速度，换句话说，什么时候我们有最佳的贝里 - 埃塞恩绑定？我们在一个相当一般的框架中研究了这个问题，并找到了（几乎）尖锐的依赖条件。该结果适用于许多不同的过程和动态系统。作为特定的突出示例，我们研究了MAP 2X MOD 1的倍增功能和一般线性组上的左随机步行。
Suppose that the (normalised) partial sum of a stationary sequence converges to a standard normal random variable. Given sufficiently moments, when do we have a rate of convergence of $n^{-1/2}$ in the uniform metric, in other words, when do we have the optimal Berry-Esseen bound? We study this question in a quite general framework and find the (almost) sharp dependence conditions. The result applies to many different processes and dynamical systems. As specific, prominent examples, we study functions of the doubling map 2x mod 1 and the left random walk on the general linear group.
