| A note on strong law of large numbers of random variables |
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| 引用本文： | LIN Zheng-yan SHEN Xin-mei. A note on strong law of large numbers of random variables[J]. 浙江大学学报(A卷英文版), 2006, 7(6): 1088-1091. DOI: 10.1631/jzus.2006.A1088 |
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| 作者姓名： | LIN Zheng-yan SHEN Xin-mei |
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| 作者单位： | Department of Mathematics，Zhejiang University，Hangzhou 310027，China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No. 10571159) and the Specialized Research Fund for the Doctoral Program of Higher Education (No. 2002335090), China |
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| 摘 要： | INTRODUCTION Chung (1947) proved the so-called “Chung’s strong law of large numbers”. Let {Xn, n∈ù} be a sequence of independent random variables with EXn=0 for all n and 0
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| 关 键 词： | SLLN 鞅差序列 A-可求和序列 随机变量 |
| 收稿时间： | 2005-11-09 |
| 修稿时间： | 2005-12-26 |
A note on strong law of large numbers of random variables |
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| Zheng-yan Lin,Xin-mei Shen. A note on strong law of large numbers of random variables[J]. Journal of Zhejiang University Science, 2006, 7(6): 1088-1091. DOI: 10.1631/jzus.2006.A1088 |
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| Authors: | Zheng-yan Lin Xin-mei Shen |
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| Affiliation: | (1) Department of Mathematics, Zhejiang University, Hangzhou, 310027, China |
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| Abstract: | In this paper, the Chung’s strong law of large numbers is generalized to the random variables which do not need the condition of independence, while the sequence of Borel functions verifies some conditions weaker than that in Chung’s theorem. Some convergence theorems for martingale difference sequence such as L p martingale difference sequence are the particular cases of results achieved in this paper. Finally, the convergence theorem for A-summability of sequence of random variables is proved, where A is a suitable real infinite matrix. Project supported by the National Natural Science Foundation of China (No. 10571159) and the Specialized Research Fund for the Doctoral Program of Higher Education (No. 2002335090), China |
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| Keywords: | Strong law of large numbers (SLLN) Martingale difference sequence A-summable sequence |
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