A note on the almost sure central limit theorem for the product of some partial sums

被引：1

作者：

Chen, Yang ^{[1
]}

Tan, Zhongquan ^{[2
]}

Wang, Kaiyong ^{[1
]}

机构：

[1] Suzhou Univ Sci & Technol, Sch Math & Phys, Suzhou 215009, Peoples R China

[2] Jiaxing Univ, Coll Math Phys & Informat Engn, Jiaxing 314001, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2014年

基金：

美国国家科学基金会;

关键词：

almost sure central limit theorem; partial sums; unbounded measurable functions; CONVERGENCE; ASYMPTOTICS;

D O I：

10.1186/1029-242X-2014-243

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (X-n) be a sequence of i.i.d., positive, square integrable random variables with E(X-1) = mu > 0, Var(X-1) = sigma(2). Denote by S-n,S-k = Sigma X-n(i=1)i - X-k and by gamma = sigma/mu the coefficient of variation. Our goal is to show the unbounded, measurable functions g, which satisfy the almost sure central limit theorem, i.e., lim(N ->infinity)1/logN Sigma=(N)(n=1)1/ng((pi S-n(k=1)n,k/(n - 1)(n)mu(n))(1/gamma root n)) = integral(infinity)(0) g(x)dF(x) a.s., where F(.) is the distribution function of the random variable eN and N is a standard normal random variable.

引用

页码：1 / 11

页数：11

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