Strong limit theorems for negatively associated random variables  with general moment conditions

doi:10.3969/j.issn.0253-2778.2015.06.005

Journal of University of Science and Technology of China ›› 2015, Vol. 45 ›› Issue (6): 460-464.DOI: 10.3969/j.issn.0253-2778.2015.06.005

• Original Paper • Previous Articles

Strong limit theorems for negatively associated random variables with general moment conditions

XIA Fengxi, DENG Xin, ZHENG Lulu, WANG Xuejun

School of Mathematical Sciences, Anhui University, Hefei 230601, China

Received:2014-06-04 Revised:2014-09-22 Accepted:2014-09-22 Online:2014-09-22 Published:2014-09-22

Abstract

Abstract: Let {X,Xn,n≥1} be a sequence of negatively associated random variables with identical distribution, {an,n≥1} be a sequence of positive constants with an/n↑. The strong law of large numbers and complete convergence for {X,Xn,n≥1} were obtained. These results are equivalent to the general moment condition ∑∞[]n=1P(|X|>an)<∞. On the other hand, the results extend the corresponding ones for pairwise independent random variables with identical distribution.

Key words: strong law of large numbers, negatively associated random variables, complete convergence

CLC Number:

O211.

XIA Fengxi, DENG Xin, ZHENG Lulu, WANG Xuejun. Strong limit theorems for negatively associated random variables with general moment conditions[J]. Journal of University of Science and Technology of China, 2015, 45(6): 460-464.

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Strong limit theorems for negatively associated random variables with general moment conditions

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