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2023•AIMS MathematicsOpen access

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

Mingzhou Xu, Xuhang Kong

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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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What this paper is about

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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Available 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.

Key concepts: Moment (physics), Convergence (economics), Mathematics, Proofs of convergence of random variables, Convergence of random variables, Random variable, Law of large numbers, Convergence tests

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