NA阵列加权乘积和的完全收敛性

设{X_(ni):1≤i≤n,n≥1}为行间NA阵列,g(x)是R~+上指数为α的正则变化函数,r>0,m为正整数,{a_(ni):1≤i≤n,n≥1}为满足条件(?)|a_(ni)|=O((g(n))~1)的实数阵列,本文得到了使sum from n=1 to ∞n~(r-1)Pr(|■multiply from j=1 to m a_(nij) X_(nij)|>ε)<∞,■ε>0成立的条件,推广并改进了Stout及王岳宝和苏淳等的结论。

COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF ARRAYS OF NA RANDOM VARIABLES

Let $\{X_{ni}:1\leq i\leq n,n\geq 1\}$ be an array of rowwise NA random variables, and let $g(x)$ be a regular function with index $\alpha$. Let $\{a_{ni}:1\leq i\leq n,n\geq 1\}$ be an array of real numbers satisfying $\max\limits_{1\leq i\leq n}|a_{ni}|=O((g(n))^{-1})$. Let $r>0$, and let $m$ be a positive integer. A set of sufficient conditions such that $\sum\limits_{n=1}^{\infty}n^{r-1} \Pr\Big(\Big|\sum\limits_{1\leq i_1<\cdots\varepsilon\Big)<\infty, \mbox{ }\forall\varepsilon>0$ are obtained. The well-known results by Stout and Wang are extended.