Complete convergence and complete integration convergence for weighted sums of arrays of rowwise $ m $-END under sub-linear expectations space

He Dong; Xili Tan; Yong Zhang; He Dong; Xili Tan; Yong Zhang

doi:10.3934/math.2023340

AIMS Mathematics

2023, Volume 8, Issue 3: 6705-6724. doi: 10.3934/math.2023340

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Research article

Complete convergence and complete integration convergence for weighted sums of arrays of rowwise $ m $-END under sub-linear expectations space

1.
College of Mathematics and Statistics, Beihua University, Jilin 132013, China
2.
School of Mathematics, Jilin University, Changchun 130012, China

Received: 19 October 2022 Revised: 10 December 2022 Accepted: 01 January 2023 Published: 09 January 2023
MSC : 60F15

In this paper, we study the complete convergence and the complete integration convergence for weighted sums of $ m $-extended negatively dependent ($ m $-END) random variables under sub-linear expectations space with the condition of $ \hat{\mathbb{E}}|X|^p\leqslant C_{\mathbb{V}}(|X|^p) < \infty $, $ p > 1/\alpha $ and $ \alpha > 3/2 $. We obtain the results that can be regarded as the extensions of complete convergence and complete moment convergence under classical probability space. In addition, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of $ m $-END random variables under the sub-linear expectations space is proved.
- sub-linear expectations space,
- rowwise $ m $-END random variables,
- complete convergence,
- complete integration convergence
Citation: He Dong, Xili Tan, Yong Zhang. Complete convergence and complete integration convergence for weighted sums of arrays of rowwise $ m $-END under sub-linear expectations space[J]. AIMS Mathematics, 2023, 8(3): 6705-6724. doi: 10.3934/math.2023340

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Abstract

In this paper, we study the complete convergence and the complete integration convergence for weighted sums of $ m $-extended negatively dependent ($ m $-END) random variables under sub-linear expectations space with the condition of $ \hat{\mathbb{E}}|X|^p\leqslant C_{\mathbb{V}}(|X|^p) < \infty $, $ p > 1/\alpha $ and $ \alpha > 3/2 $. We obtain the results that can be regarded as the extensions of complete convergence and complete moment convergence under classical probability space. In addition, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of $ m $-END random variables under the sub-linear expectations space is proved.

References

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