Complete moment convergence for partial sums of arrays of rowwise negatively superadditive dependent random variables

Abstract

In this paper, the complete moment convergence for arrays of rowwise negatively superadditive dependent (NSD, for short) random variables is established. As applications, the complete convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for arrays of rowwise NSD random variables are also obtained. Finally, a numerical simulation is carried out to verify the validity of theoretical results. The results obtained in the paper extend the corresponding ones in the literature.

Keywords:

• Complete convergence
• complete moment convergence
• Marcinkiewicz-Zygmund type strong law of large numbers
• negatively superadditive dependent random variables

MATHEMATICS Subject Classification:

• 60F15

Acknowledgments

The authors are most grateful to the Editor and three anonymous referees for carefully reading the manuscript and for valuable suggestions which helped in improving an earlier version of this paper.

Funding

This work was supported by the National Natural Science Foundation of China (11671012), the Natural Science Foundation of Anhui Province (1508085J06), the Quality Engineering Project of Anhui Province (2016jyxm0047) and the Students Innovative Training Project of Anhui University (201710357205, 201810357205).