| 次线性期望下的一般中心极限定理 |
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| 引用本文： | 兰玉婷,张宁.次线性期望下的一般中心极限定理[J].数学学报,2019,62(4):591-604. |
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| 作者姓名： | 兰玉婷 张宁 |
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| 作者单位： | 1. 上海财经大学统计与管理学院 上海 200433;
2. 山东大学数学学院 济南 250100 |
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| 基金项目： | 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） |
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| 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EXn]=εXn]=0放宽为|EXn]|+|εXn]|=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.
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| 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 |
General Central Limit Theorems Under Sublinear Expectations |
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| Yu Ting LAN,Ning ZHANG.General Central Limit Theorems Under Sublinear Expectations[J].Acta Mathematica Sinica,2019,62(4):591-604. |
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| Authors: | Yu Ting LAN Ning ZHANG |
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| Institution: | 1. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, P. R. China;
2. School of Mathematics, Shandong University, Jinan 250100, P. R. China |
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| Abstract: | 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 EXn]=EXn]=0 is replaced by|EXn]|+|EXn]|=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. |
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| Keywords: | central limit theorems convolutionary random variables G-normal distribution independent random variables sublinear expectations |
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