On the rate of convergence of Lp norms in the central limit theorem for independent random variables

被引：0

作者：

Sunklodas J. ^{[1
,2
]}

机构：

[1] Institute of Mathematics and Informatics, LT-2021 Vilnius

[2] Vilnius Gediminas Technical University, LT-2040 Vilnius

来源：

Lithuanian Mathematical Journal | 2002年 / 42卷 / 3期

关键词：

Central limit theorem; Cramér condition; Independent random variables; L[!sub]p[!/sub] norm; Lower bound; Upper bound;

D O I：

10.1023/A:1020278010643

中图分类号：

学科分类号：

摘要：

We present the upper and lower bounds of the Lp norms A np of order n-1 for all p, 1 ≤ p ≤ ∞, in the central limit theorem for independent identically distributed random variables with the finite fourth and zero first and third moments of summands. The proof of the upper estimates of the norms Anp is based on a linear differential equation formed from the characteristic function of the sum of independent random variables. © 2002 Plenum Publishing Corporation.

引用

页码：296 / 307

页数：11

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