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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2006, Vol. 7 Issue (6): 1088-1091    DOI: 10.1631/jzus.2006.A1088
Computational Mathematics & Mechanics     
A note on strong law of large numbers of random variables
LIN Zheng-yan, SHEN Xin-mei
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 Lp 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.

Key words： Strong law of large numbers (SLLN)      Martingale difference sequence      A-summable sequence     
Received: 09 November 2005     
CLC:  O211.4  
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LIN Zheng-yan
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Cite this article:

LIN Zheng-yan, SHEN Xin-mei. A note on strong law of large numbers of random variables. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(6): 1088-1091.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2006.A1088     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2006/V7/I6/1088

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