On the Strong Convergence and Complete Convergence for Pairwise NQD Random Variables

Abstract

Let $\left\{a_n,n\ge 1\right\}$ be a sequence of positive constants with $a_n/n\uparrow$ and let $\left\{X,X_n,n\ge 1\right\}$ be a sequence of pairwise negatively quadrant dependent random variables. The complete convergence for pairwise negatively quadrant dependent random variables is studied under mild condition. In addition, the strong laws of large numbers for identically distributed pairwise negatively quadrant dependent random variables are established, which are equivalent to the mild condition . Our results obtained in the paper generalize the corresponding ones for pairwise independent and identically distributed random variables.