Equivalent conditions of the complete convergence for weighted sums of NSD random variables

Abstract

In this paper, we consider the complete convergence for weighted sums of negatively superadditive-dependent (NSD) random variables without assumptions of identical distribution. Some sufficient and necessary conditions to prove the complete convergence for weighted sums of NSD random variables are presented, which extend and improve the corresponding ones of Naderi et al. As an application of the main results, the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of NSD random variables is also achieved.

Keywords:

• NSD random variables
• complete convergence
• weighted sums
• equivalent conditions

Mathematical Subject Classification (2010):

• 60F15

Acknowledgements

The authors are most grateful to the Editor in Chief Prof N. Balakrishnan and the two anonymous referees for carefully reading the manuscript and for offering some valuable suggestions and comments, which greatly enabled them to improve this paper.

Additional information

Funding

This paper is supported by the Humanities and Social Sciences Foundation for the Youth Scholars of Ministry of Education of China (15YJCZH066), the Science and Technology Plan Project of Hunan Province (2016TP1020), the Science and Technology Plan Project of Hengyang City (2017KJ183), the Nature Science Foundation of Guangxi Province (2014GXNSFBA118006), Hunan Provincial Natural Science Foundation of China (2018JJ4024) and the Construct Program of the Key Discipline in Hunan Province and University Students Research and Innovation Experiment Project of Hunan Province (C1718).