Central Limit Theorem and Diophantine Approximations

被引：7

作者：

Bobkov, Sergey G. ^{[1
]}

机构：

[1] Univ Minnesota, Sch Math, 127 Vincent Hall,206 Church St SE, Minneapolis, MN 55455 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2018年 / 31卷 / 04期

基金：

美国国家科学基金会;

关键词：

Central limit theorem; Diophantine approximation; Edgeworth expansions;

D O I：

10.1007/s10959-017-0770-4

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let F-n denote the distribution function of the normalized sum Z(n) = (X-1+ ... +X-n)/(sigma root n) of i.i.d. random variables with finite fourth absolute moment. In this paper, polynomial rates of convergence of F-n to the normal law with respect to the Kolmogorov distance, as well as polynomial approximations of F-n by the Edgeworth corrections (modulo logarithmically growing factors in n), are given in terms of the characteristic function of X-1. Particular cases of the problem are discussed in connection with Diophantine approximations.

引用

页码：2390 / 2411

页数：22

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