WOD随机变量加权和的完全收敛性

Complete convergence for weighted sums of widely orthant dependent random variables

宽象限相依变量(简称WOD变量)是一类包含独立变量,负相协变量(简称NA变量),负象限相依变量(简称NOD变量)和推广的负象限相依变量(简称END变量)在内的非常广泛的相依变量.本文利用WOD变量的Rosenthal型矩不等式和随机变量的截尾技术,在一般的条件下建立了WOD变量加权和的完全收敛性.所得结果推广了若干相依变量的相应结果.

The class of widely orthant-dependent（WOD, in short） random variables includes independent sequence, negatively associated sequence, negatively orthant dependent sequence and extended negatively dependent sequence as special cases. In this paper, the complete convergence for weighted sums of WOD random variables under some mild conditions is established by using the Rosenthal type inequality for WOD random variables and the truncation method. The result obtained in the paper generalizes the corresponding ones for some dependent random variables.