| 一类随机变量的概率不等式及几乎处处收敛性 |
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| 引用本文： | 赵婷,胡舒合,李晓琴,魏永利,王学军.一类随机变量的概率不等式及几乎处处收敛性[J].安徽大学学报(自然科学版),2010,34(1). |
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| 作者姓名： | 赵婷 胡舒合 李晓琴 魏永利 王学军 |
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| 作者单位： | 安徽大学,数学科学学院,安徽,合肥230039 |
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| 基金项目： | 国家自然科学基金资助项目(10871001);;安徽大学创新团队基金资助项目 |
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| 摘 要： | 从一个常用的概率不等式出发,在一定的矩限制条件下,得到一个随机变量序列的Hajek-Renyi型不等式,并应用此不等式证明随机变量序列部分和的几乎处处收敛性,同时给出随机变量序列部分和的推广性质和收敛速度,可以证明论文的结论优于文1]的主要结论.最后应用到随机变量序列收敛性的证明,从而推广了随机变量序列的一些收敛性质.
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| 关 键 词： | 概率不等式 几乎处处收敛性 随机变量 |
Probability inequalities and almost surely convergence properties for a class of random variables |
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| ZHAO Ting,HU Shu-he,LI Xiao-qin,WEI Yong-li,WANG Xue-jun.Probability inequalities and almost surely convergence properties for a class of random variables[J].Journal of Anhui University(Natural Sciences),2010,34(1). |
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| Authors: | ZHAO Ting HU Shu-he LI Xiao-qin WEI Yong-li WANG Xue-jun |
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| Institution: | School of Mathematical Sciences;Anhui University;Hefei 230039;China |
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| Abstract: | The authors begined with probability inequality for a class of random variable sequences,got a Hajek-Renyitype inequality for random variable sequences and the almost surely convergence properties and growth rate for partial sums of random variable sequences under moment condition,which generalized the results of Sung.Some applications for almost surely convergence of random variable sequences were given and some of them were improved. |
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| Keywords: | probability inequalities almost surely convergence random variables |
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