On the rate of convergence in the global central limit theorem for random sums of independent random variables

被引：2

作者：

Sunklodas, Jonas Kazys ^{[1
]}

机构：

[1] Vilnius Univ, Inst Math & Informat, Akad Str 4, LT-08663 Vilnius, Lithuania

来源：

LITHUANIAN MATHEMATICAL JOURNAL | 2017年 / 57卷 / 02期

关键词：

global central limit theorem; random sum; normal approximation; Stein's method; m-dependent random variables; independent random variables; tau-shifted distributions; ASYMPTOTIC NORMALITY; BOUNDS;

D O I：

10.1007/s10986-017-9358-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present upper bounds of the integral for 0 ae<currency> l ae<currency> 1 + delta, where 0 < delta ae<currency> 1, I broken vertical bar(x) is a standard normal distribution function, and Z (N) = is the normalized random sum with variance V S (N) > 0 (S (N) = X (1) + center dot center dot center dot + X (N) ) of centered independent random variables X (1) ,X (2) , . . . . The number of summands N is a nonnegative integer-valued random variable independent of X (1) ,X (2) , . . . .

引用

页码：244 / 258

页数：15

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