General results of complete convergence and complete moment convergence for weighted sums of some class of random variables

2015 ◽  
Vol 45 (15) ◽  
pp. 4494-4508 ◽  
Author(s):  
Xuejun Wang ◽  
Shuhe Hu ◽  
Andrei Volodin
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Moment Convergence

scholarly journals Complete moment convergence for Sung’s type weighted sums of ρ*-mixing random variables

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1447-1453 ◽  
Author(s):  
Wei Li ◽  
Pingyan Chen ◽  
Soo Sung
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Convergence Result ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Moment Convergence ◽  
Mixing Random Variables

In this paper, the authors study a complete moment convergence result for Sung?s type weighted sums of ?*-mixing random variables. This result extends and improves the corresponding theorem of Sung [S.H. Sung, Complete convergence for weighted sums of ?*-mixing random variables, Discrete Dyn. Nat. Soc. 2010 (2010), Article ID 630608, 13 pages].

Complete convergence and complete moment convergence for extended negatively dependent random variables

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1381-1394 ◽  
Author(s):  
Aiting Shen ◽  
Yu. Zhang ◽  
Wenjuan Wang
Keyword(s):  
Complete Convergence ◽  
Type Inequality ◽  
Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Moment Inequalities ◽  
Dependent Random Variables ◽  
Moment Convergence ◽  
Negatively Dependent Random Variables ◽  
End Random Variables

In this paper, we provide some probability and moment inequalities (especially the Marcinkiewicz-Zygmund type inequality) for extended negatively dependent (END, in short) random variables. By using the Marcinkiewicz-Zygmund type inequality and the truncation method, we investigate the complete convergence for sums and weighted sums of arrays of rowwise END random variables. In addition, the complete moment convergence for END random variables is obtained. Our results generalize and improve the corresponding ones of Wang et al. [18] and Baek and Park [2].

scholarly journals Complete moment convergence for weighted sums of negatively orthant dependent random variables

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1195-1206 ◽  
Author(s):  
Xuejun Wang ◽  
Zhiyong Chen ◽  
Ru Xiao ◽  
Xiujuan Xie
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Strong Law ◽  
Associated Random Variables ◽  
Moment Convergence ◽  
Large Numbers

In this paper, the complete moment convergence and the integrability of the supremum for weighted sums of negatively orthant dependent (NOD, in short) random variables are presented. As applications, the complete convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for NODrandom variables are obtained. The results established in the paper generalize some corresponding ones for independent random variables and negatively associated random variables.

scholarly journals On complete and complete moment convergence for weighted sums of widely orthant dependent random variables

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5347-5359 ◽  
Author(s):  
Caoqing Wu ◽  
Mingming Ning ◽  
Aiting Shen
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Dependent Random Variables ◽  
Moment Convergence ◽  
Identical Distribution ◽  
Widely Orthant Dependent

In this article, the complete convergence for weighted sums of widely orthant dependent (WOD, in short) random variables without identical distribution is investigated. In addition, the complete moment convergence for weighted sums of WOD random variables is also obtained. The results obtained in the paper generalize some corresponding ones for some dependent random variables.

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