scholarly journals Convergence for sums of i.i.d. random variables under sublinear expectations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mingzhou Xu ◽  
Kun Cheng
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Moment Convergence ◽  
Equivalent Conditions ◽  
Independent Identically Distributed

AbstractIn this paper, we obtain equivalent conditions of complete moment convergence of the maximum for partial weighted sums of independent identically distributed random variables under sublinear expectations space. The results obtained in the paper are extensions of the equivalent conditions of complete moment convergence of the maximum under classical linear expectation space.

scholarly journals Equivalent Conditions of Complete p th Moment Convergence for Weighted Sums of I. I. D. Random Variables under Sublinear Expectations

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Mingzhou Xu ◽  
Kun Cheng
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Moment Inequality ◽  
Moment Convergence ◽  
Equivalent Conditions ◽  
Independent Identically Distributed

We investigate the complete p th moment convergence for weighted sums of independent, identically distributed random variables under sublinear expectations space. Using moment inequality and truncation methods, we prove the equivalent conditions of complete p th moment convergence of weighted sums of independent, identically distributed random variables under sublinear expectations space, which complement the corresponding results obtained in Guo and Shan (2020).

Complete moment convergence forweighted sums of pairwise negatively quadrant dependent random variables

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3459-3471
Author(s):  
Mingming Zhao ◽  
Shengnan Ding ◽  
Di Zhang ◽  
Xuejun Wang
Keyword(s):  
Theoretical Result ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Dependent Random Variables ◽  
Moment Convergence

In this article, the complete moment convergence for weighted sums of pairwise negatively quadrant dependent (NQD, for short) random variables is studied. Several sufficient conditions to prove the complete moment convergence for weighted sums of NQD random variables are presented. The results obtained in the paper extend some corresponding ones in the literature. The simulation is also presented which can verify the validity of the theoretical result.

scholarly journals Complete integration convergence for arrays of rowwise extended negatively dependent random variables under the sub-linear expectations

2021 ◽  
Vol 6 (11) ◽  
pp. 12166-12181
Author(s):  
Shuyan Li ◽  
◽  
Qunying Wu
Keyword(s):  
Limit Theorems ◽  
Probability Space ◽  
Random Variables ◽  
Weighted Sums ◽  
Complete Moment Convergence ◽  
Dependent Random Variables ◽  
Complete Integration ◽  
Moment Convergence ◽  
Negatively Dependent Random Variables

<abstract><p>Limit theorems of sub-linear expectations are challenging field that has attracted widespread attention in recent years. In this paper, we establish some results on complete integration convergence for weighted sums of arrays of rowwise extended negatively dependent random variables under sub-linear expectations. Our results generalize the complete moment convergence of the probability space to the sub-linear expectation space.</p></abstract>

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