Communications of the
Korean Mathematical Society CKMS

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