中文摘要：

设{Xn,n≥1}为被随机变量X随机控制的AANA（asymptotically almost negatively associated）随 机变量序列，{an,n≥1}是正常数列．在适当的矩条件下，研究了AANA随机变量加权和1≤k≤nmaxa-1nk∑i-1Xi的完全收敛性．作为该结果的应用，得到了一些关于AANA随机变量序列完全收敛性的新结果．

英文摘要：

Let {Xn,n≥ 1} be a sequence of asymptotically almost negatively associated （AANA, in short） random variables which is stochastically dominated by a random variable X , and {an,n ≥ 1} be a sequence of positive constants. Under some suitable moment conditions, we mainly studied the complete convergence for weighted sums1≤k≤nmaxa-1nk∑i-1Xiof AANA random variables. As to applications, we presented some new results on complete convergence for AANA random variables.