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.

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.

Equivalent conditions of complete convergence for weighted sums of ANA random variables

2018 ◽  
Vol 68 (6) ◽  
pp. 1495-1505
Author(s):  
Haiwu Huang
Keyword(s):  
Convergence Theorem ◽  
Complete Convergence ◽  
Random Variables ◽  
Weighted Sums ◽  
Negatively Associated ◽  
Complete Convergence Theorem ◽  
Equivalent Conditions

Abstract In this paper, the author investigates the complete convergence for weighted sums of asymptotically negatively associated (ANA) random variables with different distributions, and obtains some equivalent conditions of complete convergence theorem for weighted sums as well as summation of ANA cases. These results generalize and improve the corresponding ones obtained by Baum and Katz (1965), Peligrad and Gut (1999) and Cai (2006), respectively.

scholarly journals On Some Conditions for Strong Law of Large Numbers for Weighted Sums of END Random Variables under Sublinear Expectations

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Xiaochen Ma ◽  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables ◽  
Large Numbers ◽  
End Random Variables

In this article, we research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our consequences contain the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for weighted sums of extended negatively dependent random variables. Furthermore, our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context.

scholarly journals Complete Convergence for END Random Variables under Sublinear Expectations

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Qunying Wu
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Weighted Sums ◽  
Partial Sums ◽  
Convergence Theorems ◽  
Classical Probability ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables ◽  
Probability Spaces ◽  
End Random Variables

In this paper, the complete convergence theorems of partial sums and weighted sums for extended negatively dependent random variables in sublinear expectation spaces have been studied and established. Our results extend the corresponding results of classical probability spaces to the case of sublinear expectation spaces.

scholarly journals Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums ofρ~-Mixing Random Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chongfeng Lan
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Strong Law ◽  
Large Numbers ◽  
Sufficient And Necessary Conditions ◽  
Complete Convergence Theorem ◽  
Mixing Random Variables ◽  
Equivalent Conditions

The equivalent conditions of complete convergence are established for weighted sums ofρ~-mixing random variables with different distributions. Our results extend and improve the Baum and Katz complete convergence theorem. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequence ofρ~-mixing random variables is obtained.

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