NA阵列加权乘积和的完全收敛性

COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF ARRAYS OF NA RANDOM VARIABLES

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。

Let {xni：l≤i≤n,n≥1} be an array of rowwise NA random variables,and let g（x） be a regular function with index α. Let {ani：1≤i≤n,n≥1} be an array of real numbers satisfying max 1≤i≤n,n≥1 ani = O（（g（n））^-1）. Let r〉0, and let m be a positive integer. A set of sufficient conditions such that ∑ 1≤i1〈…〈im≤n Л j=1 ^m anij,Xnij〉ε）〈∞,ε〉0 are obtained. The well-known results by Stout and Wang are extended.