‘LIMITING BEHAVIOUR FOR ARRAYS OF UPPER EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES’

2015 ◽  
Vol 92 (3) ◽  
pp. 524-524 ◽  
Author(s):  
JOÃO LITA DA SILVA
Keyword(s):  
Random Variables ◽  
Dependent Random Variables ◽  
Negatively Dependent Random Variables ◽  
Limiting Behaviour

LIMITING BEHAVIOUR FOR ARRAYS OF UPPER EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES

2015 ◽  
Vol 92 (1) ◽  
pp. 159-167 ◽  
Author(s):  
JOÃO LITA DA SILVA
Keyword(s):  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Dependent Random Variables ◽  
Triangular Arrays ◽  
Negatively Dependent Random Variables ◽  
Limiting Behaviour

For triangular arrays $\{X_{n,k}:1\leqslant k\leqslant n,n\geqslant 1\}$ of upper extended negatively dependent random variables weakly mean dominated by a random variable $X$ and sequences $\{b_{n}\}$ of positive constants, conditions are given to guarantee an almost sure finite upper bound to $\sum _{k=1}^{n}(X_{n,k}-\mathbb{E}X_{n,k})/\!\sqrt{b_{n}\,\text{Log}\,n}$, where $\text{Log}\,n:=\max \{1,\log n\}$, thus getting control over the limiting rate in terms of the prescribed sequence $\{b_{n}\}$ and permitting us to weaken or strengthen the assumptions on the random variables.

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 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.

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