| 一个推广的Borel强大数定律的改进 |
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| 引用本文： | 任春光,胡舒合,李旭,刘小涛. 一个推广的Borel强大数定律的改进[J]. 安徽大学学报(自然科学版), 2011, 0(3) |
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| 作者姓名： | 任春光 胡舒合 李旭 刘小涛 |
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| 作者单位： | 安徽大学数学科学学院; |
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| 基金项目： | 国家自然科学基金资助项目(10871001); 安徽大学青年科研基金资助项目(2009QN011A) |
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| 摘 要： | Borel通过研究Bernoulli试验,首先给出了其强大数定律,已有文献给出了一个推广的Borel强大数定律.作者改进了这个结果,将其中的条件dn=O(1/n)减弱为dn=O(1/nα),α>0.另外,将此结果推广到有界的随机变量序列的情形,给出其Borel强大数定律.
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| 关 键 词： | Bernoulli大数定律 推广的Borel强大数定律 随机序列 |
Some improvements to an extended Borel strong law of large numbers |
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| REN Chun-guang,HU Shu-he,LI Xu,LIU Xiao-tao. Some improvements to an extended Borel strong law of large numbers[J]. Journal of Anhui University(Natural Sciences), 2011, 0(3) |
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| Authors: | REN Chun-guang HU Shu-he LI Xu LIU Xiao-tao |
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| Affiliation: | REN Chun-guang,HU Shu-he,LI Xu,LIU Xiao-tao (School of Mathematical Sciences,Anhui University,Hefei 230039,China) |
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| Abstract: | Borel firstly obtained the strong law of large numbers by studing the Bernoulli trails,and an extended Borel strong law of large numbers was given in some references.We improved this extended Borel strong law of large numbers,whose condition dn=O(1/n) was weakened to dn=O(1/nα),α>0.In addition,we generalized these results to the case of the bounded random variables and obtianed their Borel strong law of large numbers. |
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| Keywords: | Bernoulli strong law of large numbers an extended Borel strong law of large numbers random sequence |
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