Complete convergence for weighted sums of a class of random variables

Abstract

Let $\{a_{ni},1\leq i\leq n,n\geq1\}$ be an array
of real numbers and $\{X_n, n\geq1\}$ be a sequence of random
variables satisfying the Rosenthal type inequality, which is
stochastically dominated by a random variable $X$. Under mild
conditions, we present some results on complete convergence for
weighted sums $\sum_{i=1}^n a_{ni} X_i$ of random variables
satisfying the Rosenthal type inequality. The results obtained in
the paper generalize some known ones in the literatures.