Mean Convergence Theorems for Weighted Sums of Arrays of Residually h-integrable Random Variables Concerning the Weights under Dependence Assumptions

2008 ◽  
Vol 103 (3) ◽  
pp. 221-234 ◽  
Author(s):  
Demei Yuan ◽  
Bao Tao
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Convergence Theorems ◽  
Mean Convergence

Some mean convergence theorems for weighted sums of Banach space valued random elements

Stochastics ◽  
2021 ◽  
pp. 1-19
Author(s):  
Pingyan Chen ◽  
Manuel Ordóñez Cabrera ◽  
Andrew Rosalsky ◽  
Andrei Volodin
Keyword(s):  
Banach Space ◽  
Weighted Sums ◽  
Convergence Theorems ◽  
Mean Convergence ◽  
Random Elements

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 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 of PNQD Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Qunying Wu
Keyword(s):  
Complete Convergence ◽  
Necessary Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Moment Inequality ◽  
Convergence Theorems ◽  
Limit Theory ◽  
Sufficient And Necessary Conditions

The complete convergence for pairwise negative quadrant dependent (PNQD) random variables is studied. So far there has not been the general moment inequality for PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection that contains relationship to overcome the difficulties that there is no general moment inequality. Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables are obtained. Our results generalize and improve those on complete convergence theorems previously obtained by Baum and Katz (1965) and Wu (2002).

scholarly journals Complete convergence for weighted sums of weakly negative dependent of random variables

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3177-3186
Author(s):  
H. Naderi ◽  
M. Amini ◽  
A. Bozorgnia
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Weighted Sums ◽  
Convergence Theorems ◽  
Random Weighting

Some basic theoretical properties and complete convergence theorems for weighted sums of weakly negative dependent are provided and applied to random weighting estimate. Moreover, various examples are presented.

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