NA列自正则某些部分和乘积的几乎处处中心极限定理

doi:10.6040/j.issn.1671-9352.0.2015.106

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (2): 50-57.doi: 10.6040/j.issn.1671-9352.0.2015.106

NA列自正则某些部分和乘积的几乎处处中心极限定理

徐锋,吴群英^*

桂林理工大学理学院, 广西桂林 541004

收稿日期:2015-03-12 出版日期:2016-02-16 发布日期:2016-03-11
通讯作者: 吴群英(1961— ),女,博士,教授,研究方向为概率统计.E-mail:wqy666@glut.edu.cn E-mail:xufeng34@163.com
作者简介:徐锋(1989— ),男,硕士生,研究方向为概率极限理论. E-mail:xufeng34@163.com
基金资助:
国家自然科学基金资助项目(11361019);广西自然科学基金重点项目(2013GXNSFDA019001)

Almost sure central limit theorem for self-normalized products of some partial sums of NA random variables

XU Feng, WU Qun-ying^*

College of Science, Guilin University of Technology, Guilin 541004, Guangxi, China

Received:2015-03-12 Online:2016-02-16 Published:2016-03-11

摘要/Abstract

摘要： 设{X,X_n}_n∈N是平稳正的负相关(negatively associated, NA)随机变量序列,证明自正则某些部分和乘积(∏^k_i=1(S_k,i/((k-1)μ)))^μ/(βV_k)的几乎处处中心极限定理,其中β>0为一常数,E(X)=μ, S_k,i=∑^k_j=1X_j-X_i, 1≤i≤k, V²_k=∑^k_i=1(X_i-μ)²。获得的结果不仅将其权重进行了推广而且也扩大了随机变量的范围。

关键词: 部分和乘积, 几乎处处中心极限定理, 自正则, NA列

Abstract: Let {X,X_n}_n∈N be a stationary sequence of NA positive random variables. We proved an almost sure central limit theorem for the self-normalized products of some partial sums(∏^k_i=1(S_k,i/((k-1)μ)))^μ/(βV_k), where β>0 was a constant, E(X)=μ, S_k,i=∑^k_j=1X_j-X_i, 1≤i≤k, V2_k=∑^k_i=1(X_i-μ)2. The results generalize not only on the weigh of the almost sure central limit theorem but also in the range of random variables.

Key words: self-normalized, products of sums, almost sure central limit theorem, NA sequences

中图分类号:

O211

徐锋,吴群英. NA列自正则某些部分和乘积的几乎处处中心极限定理[J]. 山东大学学报（理学版）, 2016, 51(2): 50-57.

XU Feng, WU Qun-ying. Almost sure central limit theorem for self-normalized products of some partial sums of NA random variables[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 50-57.

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NA列自正则某些部分和乘积的几乎处处中心极限定理

Almost sure central limit theorem for self-normalized products of some partial sums of NA random variables

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