Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables

The complete convergence for pairwise negative quadrant dependent PNQD random variables is studied. So far there has not been the generalmoment inequality for PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection that contains relationship to overcome the difficulties that there is no general moment inequality. Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables are obtained. Our results generalize and improve those on complete convergence theorems previously obtained by Baum and Katz 1965 and Wu 2002 .