Equivalent conditions of complete convergence and complete moment convergence for END random variables

2018 ◽  
Vol 39 (1) ◽  
pp. 83-96 ◽  
Author(s):  
Aiting Shen ◽  
Mei Yao ◽  
Benqiong Xiao
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Moment Convergence ◽  
End Random Variables ◽  
Equivalent Conditions

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 arrays of rowwise END random variables

2014 ◽  
Vol 49 (2) ◽  
pp. 447-466 ◽  
Author(s):  
Yongfeng Wu ◽  
◽  
Manuel Ordóñez Cabrera ◽  
Andrei Volodin ◽  
◽  
...  
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Moment Convergence ◽  
End Random Variables

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.

scholarly journals Complete Convergence for Moving Average Process of Martingale Differences

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Wenzhi Yang ◽  
Shuhe Hu ◽  
Xuejun Wang
Keyword(s):  
Complete Convergence ◽  
Moving Average ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Average Process ◽  
Moving Average Process ◽  
Martingale Differences ◽  
Moment Convergence ◽  
Moving Process

Under some simple conditions, by using some techniques such as truncated method for random variables (see e.g., Gut (2005)) and properties of martingale differences, we studied the moving process based on martingale differences and obtained complete convergence and complete moment convergence for this moving process. Our results extend some related ones.

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