Maximal inequalities and strong law of large numbers for AANA sequences
Commun. Korean Math. Soc. 2011 Vol. 26, No. 1, 151-161
https://doi.org/10.4134/CKMS.2011.26.1.151
Printed March 1, 2011
Wang Xuejun, Hu Shuhe, Li Xiaoqin, and Yang Wenzhi
Anhui University, Anhui University, Anhui University, Anhui University
Abstract : Let $\{X_n, n\geq1\}$ be a sequence of asymptotically almost negatively associated random variables and $S_n=\sum_{i=1}^nX_i$. In the paper, we get the precise results of H\'ajek-R\'enyi 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\'ajek-R\'enyi inequality, asymptotically almost negatively associated sequence, strong law of large numbers, large deviation
MSC numbers : 60E10, 60F15, 60F10
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