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http://dx.doi.org/10.4134/CKMS.2011.26.1.151

MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES  

Xuejun, Wang (SCHOOL OF MATHEMATICAL SCIENCE ANHUI UNIVERSITY)
Shuhe, Hu (SCHOOL OF MATHEMATICAL SCIENCE ANHUI UNIVERSITY)
Xiaoqin, Li (SCHOOL OF MATHEMATICAL SCIENCE ANHUI UNIVERSITY)
Wenzhi, Yang (SCHOOL OF MATHEMATICAL SCIENCE ANHUI UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.26, no.1, 2011 , pp. 151-161 More about this Journal
Abstract
Let {$X_n$, $n{\geq}1$} be a sequence of asymptotically almost negatively associated random variables and $S_n=\sum^n_{i=1}X_i$. In the paper, we get the precise results of H$\acute{a}$jek-R$\acute{e}$nyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of $S_n$ for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.
Keywords
H$\acute{a}$jek-R$\acute{e}$nyi inequality; asymptotically almost negatively associated sequence; strong law of large numbers; large deviation;
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