Complete moment convergence for arrays of rowwise NSD random variables

Abstract

In this paper, the complete convergence and complete moment convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are investigated. Some sufficient conditions to prove the complete convergence and the complete moment convergence are presented. The results obtained in the paper generalize and improve some corresponding ones for independent random variables and negatively associated random variables.

Keywords:

• Negatively superadditive dependent random variables
• complete convergence
• complete moment convergence

AMS Subject Classification:

• 60F15

Acknowledgements

The authors are most grateful to the Editor-in-Chief, Associated Editor and anonymous referees for careful reading of the manuscript and valuable suggestions which helped in improving an earlier version of this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by the National Natural Science Foundation of China [grant number 11201001], [grant number 11501004], [grant number 11501005]; the Natural Science Foundation of Anhui Province (1508085J06, 1308085QA03); the Provincial Natural Science Research Project of Anhui Colleges (KJ2015A018); the Open Project of School of Mathematical Sciences, Anhui University (ADSY201503); the Quality Improvement Projects for Undergraduate Education of Anhui University (ZLTS2015035); the Students Innovative Training Project of Anhui University (201510357116).