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ABSTRACT
In this paper, we first establish the complete convergence for weighted sums of widely orthant-dependent (WOD, in short) random variables by using the Rosenthal type maximal inequality. Based on the complete convergence, we further study the complete moment convergence for weighted sums of arrays of rowwise WOD random variables which is stochastically dominated by a random variable X. The results obtained in the paper generalize the corresponding ones for some dependent random variables.
MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors are most grateful to the Editor-in-Chief Prof. N. Balakrishnan and two anonymous referees for careful reading of the manuscript and 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, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1508085J06, 1608085QA02), the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005), the Foundation of Anhui Educational Committee (KJ2013Z225) and the Students Innovative Training Project of Anhui University (ZLTS2015138).