Note on complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations

Mingzhou Xu; Xuhang Kong; Mingzhou Xu; Xuhang Kong

doi:10.3934/math.2023428

AIMS Mathematics

2023, Volume 8, Issue 4: 8504-8521. doi: 10.3934/math.2023428

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Research article

Note on complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations

Mingzhou Xu ^,,
Xuhang Kong

School of Information Engineering, Jingdezhen Ceramic University, Jingdezhen 333403, China

Received: 12 November 2022 Revised: 18 January 2023 Accepted: 28 January 2023 Published: 06 February 2023
MSC : 60F15, 60F05

In this article, we study the complete convergence and the complete moment convergence for negatively dependent (ND) random variables under sub-linear expectations. Under proper conditions of the moment of random variables, we establish the complete convergence and the complete moment convergence. As applications, we obtain the Marcinkiewcz-Zygmund type strong law of large numbers of ND random variables under sub-linear expectations. The results here generalize the corresponding ones in classic probability space to those under sub-linear expectations.
- negatively dependent random variables,
- complete convergence,
- complete moment convergence,
- sub-linear expectations
Citation: Mingzhou Xu, Xuhang Kong. Note on complete convergence and complete moment convergence for negatively dependent random variables under sub-linear expectations[J]. AIMS Mathematics, 2023, 8(4): 8504-8521. doi: 10.3934/math.2023428

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Abstract

In this article, we study the complete convergence and the complete moment convergence for negatively dependent (ND) random variables under sub-linear expectations. Under proper conditions of the moment of random variables, we establish the complete convergence and the complete moment convergence. As applications, we obtain the Marcinkiewcz-Zygmund type strong law of large numbers of ND random variables under sub-linear expectations. The results here generalize the corresponding ones in classic probability space to those under sub-linear expectations.

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