| 相协随机变量部分和的几乎处处收敛性和强大数定律 |
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| 引用本文： | 王学军,胡舒合,马松林. 相协随机变量部分和的几乎处处收敛性和强大数定律[J]. 合肥工业大学学报(自然科学版), 2007, 30(5): 637-640 |
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| 作者姓名： | 王学军 胡舒合 马松林 |
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| 作者单位： | 安徽大学,数学与计算科学学院,安徽,合肥,230039;安徽大学,数学与计算科学学院,安徽,合肥,230039;安徽大学,数学与计算科学学院,安徽,合肥,230039 |
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| 摘 要： | 文章基于相协随机变量序列的Hajek-Renyi不等式和事件序列的Chung-Erdos不等式,利用Krone-cker引理和Borel-Cantelli引理,给出相协随机变量序列部分和的几乎处处收敛性和强大数定律型的结果,推广和改进了吴爱娟论文中定理2和定理3的结果。作为其特例,得到了独立情形下经典的Kolmogorov强大数定律。
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| 关 键 词： | Hajek-Renyi不等式 相协随机变量序列 几乎处处收敛 强大数定律 |
| 文章编号： | 1003-5060(2007)05-0637-04 |
| 修稿时间： | 2006-04-19 |
Almost sure convergence and a strong law of large numbers for the partial sum of associated random variable sequences |
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| WANG Xue-jun,HU Shu-he,MA Song-lin. Almost sure convergence and a strong law of large numbers for the partial sum of associated random variable sequences[J]. Journal of Hefei University of Technology(Natural Science), 2007, 30(5): 637-640 |
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| Authors: | WANG Xue-jun HU Shu-he MA Song-lin |
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| Abstract: | This paper presents some almost sure convergence properties and a strong law of large numbers for the partial sum of associated random variable sequences based on the Hajek-Renyi inequality for associated random variables and the Chung-Erdos inequality for event sequences using the Kronecker lemma and the Borel-Cantelli lemma,which generalize and improve the result in related literature.As a special case,the classical Kolmogorov strong law of large numbers for independent random variables is given. |
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| Keywords: | Hajek-Renyi inequality associated random variable sequence almost sure convergence strong law of large numbers |
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