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.

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 convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1093-1104
Author(s):  
Qunying Wu ◽  
Yuanying Jiang
Keyword(s):  
Probability Space ◽  
Complete Convergence ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Convergence Theorems ◽  
Dependent Random Variables ◽  
Moment Convergence ◽  
Negatively Dependent Random Variables

This paper we study and establish the complete convergence and complete moment convergence theorems under a sub-linear expectation space. As applications, the complete convergence and complete moment convergence for negatively dependent random variables with CV (exp (ln? |X|)) < ?, ? > 1 have been generalized to the sub-linear expectation space context. We extend some complete convergence and complete moment convergence theorems for the traditional probability space to the sub-linear expectation space. Our results generalize corresponding results obtained by Gut and Stadtm?ller (2011), Qiu and Chen (2014) and Wu and Jiang (2016). There is no report on the complete moment convergence under sub-linear expectation, and we provide the method to study this subject.

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