Complete convergence theorem for negatively dependent random variables under sub-linear expectations

2020 ◽  
pp. 1-14
Author(s):  
Binxia Chen ◽  
Qunying Wu
Keyword(s):  
Convergence Theorem ◽  
Complete Convergence ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Negatively Dependent Random Variables ◽  
Complete Convergence Theorem

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 Some Types of Convergence for Negatively Dependent Random Variables under Sublinear Expectations

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Ruixue Wang ◽  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Complete Convergence ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Weighted Sums ◽  
Convergence Theorems ◽  
Dependent Random Variables ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables

In this paper, we research complete convergence and almost sure convergence under the sublinear expectations. As applications, we extend some complete and almost sure convergence theorems for weighted sums of negatively dependent random variables from the traditional probability space to the sublinear expectation space.

scholarly journals Complete Convergence for Weighted Sums of Widely Acceptable Random Variables under Sublinear Expectations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Rong Hu ◽  
Qunying Wu
Keyword(s):  
Convergence Theorem ◽  
Probability Space ◽  
Complete Convergence ◽  
Choquet Integral ◽  
Random Variables ◽  
Weighted Sums ◽  
Sublinear Expectation ◽  
Acceptable Random Variables ◽  
Complete Convergence Theorem

Using different methods than the probability space, under the condition that the Choquet integral exists, we study the complete convergence theorem for weighted sums of widely acceptable random variables under sublinear expectation space. We proved corresponding theorem which was extended to the sublinear expectations’ space from the probability space, and similar results were obtained.

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