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J. Korean Math. Soc. 2017; 54(3): 877-896
Online first article January 17, 2017 Printed May 1, 2017
https://doi.org/10.4134/JKMS.j160293
Copyright © The Korean Mathematical Society.
On complete convergence and complete moment convergence for a class of random variables
Xuejun Wang and Yi Wu
Anhui University, Anhui University
In this paper, the complete convergence and complete moment convergence for a class of random variables satisfying the Rosenthal type inequality are investigated. The sufficient and necessary conditions for the complete convergence and complete moment convergence are provided. As applications, the Baum-Katz type result and the Marcinkie\-wicz-Zygmund type strong law of large numbers for a class of random variables satisfying the Rosenthal type inequality are established. The results obtained in the paper extend the corresponding ones for some dependent random variables.
Keywords: complete convergence, complete moment convergence, stochastic domination, Rosenthal type inequality
MSC numbers: 60F15
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