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数学进展 - 2020, Vol. 49(4): 497-511
研究论文
次线性期望空间下END随机变量加权和的极限定理
Limiting Behavior of Weighted Sums of Extended Negatively Dependent Random Variables under Sublinear Expectations

马晓晨, 吴群英
MA Xiaochen*, WU Qunying**

桂林理工大学理学院, 桂林, 广西, 541004
College of Science, Guilin University of Technology, Guilin, Guangxi, 541004, P. R. China

收稿日期: 2019-06-21
出版日期: 2020-08-11
2020, Vol. 49(4): 497-511
DOI: 10.11845/sxjz.2019071b


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摘要 本文研究了在次线性期望空间中END序列的强大数定律(SLLN)非常广泛的形式. 在随机变量上积分$C_{\mathbb{V}}(\varphi^{-}(|X|))<\infty$存在的条件下(其中$\varphi(x)=x^{\frac{1}{\beta}}l(x)$), 获得了次线性期望空间中END序列的强大数定律(SLLN). 此外, 我们的结果将[J. Math. Res. Exposition, 2011, 31(6): 1081-1091]中的相应结果推广到了次线性期望空间.
关键词 次线性期望强大数定律END随机变量    
Abstract:In this article, our purpose is to establish the very extensive version of the strong law of large numbers (SLLN) of extended negatively dependent (END) random variables in the general sublinear expectation space. We obtain SLLN for END random variables under sublinear expectation with the upper integral condition of $C_{\mathbb{V}}(\varphi^{-}(|X|))<\infty$, where $\varphi(x)=x^{\frac{1}{\beta}}l(x)$. In addition, the results generalize corresponding results in [J. Math. Res. Exposition, 2011, 31(6): 1081-1091] to the sublinear expectations.
Key wordssublinear expectation    strong law of large numbers    END random variables
PACS:  O211.4  
通讯作者: E-mail: * 1315374078@qq.com; ** wqy666@glut.edu.cn   
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