On Complete Moment Convergence for Randomly Weighted Sums of NSD Random Variables

Abstract

In this paper, we investigate the complete moment convergence and complete convergence for randomly weighted sums of negatively superadditive dependent (NSD, in short) random variables. The results obtained in the paper generalize the convergence theorem for constant weighted sums to randomly weighted sums of dependent random variables. In addition, strong law of large numbers for NSD sequence is obtained. AMS subject classifications: 60F15.