COMPLETE CONVERGENCE FOR ARRAY OF ROWWISE DEPENDENT RANDOM VARIABLES

Let {$X_{ni}|1\;{\le}\;i\;{\le}\;n$, $n\;{\ge}\;1$} be an array of rowwise negatively associated random variables and let $\alpha$ > 1/2, 0 < p < 2 ${\alpha}p\;{\ge}\;1$. In this paper we discuss $n^{{\alpha}p-2}h(n)$ max $_{1\;{\le}\;k{\le}n}\;|\;{\sum}^k_{i=1}\;X_{ni}|/n^{\alpha}\;{\to}\;0$ completely as $n\;{\to}\;{\infty}$ under not necessarily identically distributed with a suitable conditions and h(x) > 0 is a slowly varying function as $x\;{\to}\;{\infty}$. In addition, we obtained that $n^{{\alpha}p-2}h(n)$ max $_{1\;{\le}\;k{\le}n}\;|\;{\sum}^k_{i=1}\;X_{ni}|/n^{\alpha}\;{\to}\;0$ completely as $n\;{\to}\;{\infty}$ if and only if $E|X_{11}|^ph(|X_{11}|^{1/\alpha})\;<\;{\infty}$ and $EX_{11}\;=\;0$ under identically distributed case and some corollaries are obtained.