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次线性期望下的一般中心极限定理
General Central Limit Theorems Under Sublinear Expectations
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]=E[Xn]=0放宽为|E[Xn]|+|E[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]=E[Xn]=0 is replaced by|E[Xn]|+|E[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.
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 {{custom_keyword}} /
central limit theorems / convolutionary random variables / G-normal distribution / independent random variables / sublinear expectations {{custom_keyword}} /
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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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