摘要
受Peng-中心极限定理的启发,本文主要应用G-正态分布的概念,放宽Peng-中心极限定理的条件,在次线性期望下得到形式更为一般的中心极限定理.首先,将均值条件E[Xn]=ε[Xn]=0放宽为|E[Xn]|+|ε[Xn]|=O(1/n);其次,应用随机变量截断的方法,放宽随机变量的2阶矩与2+δ阶矩条件;最后,将该定理的Peng-独立性条件进行放宽,得到卷积独立随机变量的中心极限定理.
Inspired by the central limit theorem established by Peng, we investigate the generalized central limit theorem under sublinear expectations based on three weaker conditions with the notion of G-normal distribution. Initially, the condition E[Xn]=ε[Xn]=0 is replaced by|E[Xn]|+|ε[Xn]|=O(1/n). Furthermore, the original 2-nd and (2+δ)-th moments conditions are weakened through the truncation of random variables. Finally, we develop the theorem for convolutionary random variables, which can be seen as a generalization of Peng-independence.
作者
兰玉婷
张宁
Yu Ting LAN;Ning ZHANG(School of Statistics and Management,Shanghai University of Finance and Economics,Shanghai 200433,P.R.China;School of Mathematics,Shandong University,Jinan 250100,P.R.China)
出处
《数学学报（中文版）》
CSCD
北大核心
2019年第4期591-604,共14页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(11601280)
上海财经大学中央高校基本科研业务费专项资金(2017110072)
关键词
中心极限定理
卷积独立随机变量
G-正态分布
独立随机变量
次线性期望
central limit theorems
convolutionary random variables
G-normal distribution
independent random variables
sublinear expectations
