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http://dx.doi.org/10.4134/JKMS.j160293

ON COMPLETE CONVERGENCE AND COMPLETE MOMENT CONVERGENCE FOR A CLASS OF RANDOM VARIABLES  

Wang, Xuejun (School of Mathematical Sciences Anhui University)
Wu, Yi (School of Mathematical Sciences Anhui University)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.3, 2017 , pp. 877-896 More about this Journal
Abstract
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 Marcinkiewicz-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;
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