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 general moment 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)

Complete integral convergence for weighted sums of negatively dependent random variables under sub-linear expectations

In the paper, the complete convergence and complete integral convergence for weighted sums of negatively dependent random variables under the sub-linear expectations are established. The results in the paper extend some complete moment convergence theorems from the classical probability space to the situation of sub-linear expectation space