Equivalent Conditions of Complete Convergence and Complete Moment Convergence for END Random Variables

Citation:

Aiting SHEN,Mei YAO,Benqiong XIAO.Equivalent Conditions of Complete Convergence and Complete Moment Convergence for END Random Variables[J].Chinese Annals of Mathematics B,2018,39(1):83~96
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Authors:

Aiting SHEN; Mei YAO;Benqiong XIAO

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11501004, 11501005, 11526033), the Natural Science Foundation of Anhui Province (No.1508085J06), the Key Projects for Academic Talent of Anhui Province (No.gxbjZD2016005), the Provincial Natural Science Research Project of Anhui Colleges (No.KJ2015A018), the Open Project of School of Mathematical Sciences, Anhui University (No.ADSY201503), the Quality Engineering Project of Anhui Province (No.2015jyxm045) and the Quality Improvement Projects for Undergraduate Education of Anhui University (No.ZLTS2015035).
Abstract: In this paper, the complete convergence and the complete moment convergence for extended negatively dependent (END, in short) random variables without identical distribution are investigated. Under some suitable conditions, the equivalence between the moment of random variables and the complete convergence is established. In addition, the equivalence between the moment of random variables and the complete moment convergence is also proved. As applications, the Marcinkiewicz-Zygmund-type strong law of large numbers and the Baum-Katz-type result for END random variables are established. The results obtained in this paper extend the corresponding ones for independent random variables and some dependent random variables.

Keywords:

Extended negatively dependent random variables, Completeconvergence, Complete moment convergence

Classification:

60F15
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