行为NA随机变量阵列加权和完全收敛性的等价条件

Equivalent Conditions of Complete Convergence for Weighted Sums for Arrays of Row-Wise Negatively Associated Random Variables

本文利用Chen等^([14])所获得的随机变量阵列加权和完全收敛的充分条件,建立了随机变量阵列加权和完全收敛的等价条件,推广了Liang^([11])的结果.同时我们采用和Liang不同的证明方法,极大地简化了证明过程,并在此基础上拓展了Gut^([13])关于独立随机变量Cesaro和的完全收敛性结论.

In this article, applying the result of complete convergence for negatively associated （NA） random variables which is obtained by Chen et al. the equivalent conditions of complete convergence for weighted sums of arrays of row-wise negatively associated random variables is investigated. As a result, the corresponding results of Liang is generalized, moreover, the proof procedure is simplified greatly which is different from truncation method of Liang＇s. Thus, Gut＇s result on Ceshro summation of i.i.d. random variables is extended.