Baum-Katz-type complete and complete moment convergence theorems for the maximal weighted sums under the sub-linear expectations

Fengxiang Feng and Haiwu Huang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 16, 5191-5209

Abstract: In this article, we establish Baum-Katz-type complete and complete moment convergence theorems for the maximal weighted sums of independent and identically distributed random variables in a sub-linear expectation space (Ω,H,Ê). Our results extend the corresponding complete convergence and complete moment results of probability spaces to sub-linear expectation spaces. Our results are very extensive, and we can obtain a series of complete and complete moment convergence results from our theorems. As an application of our theorem, we obtain the strong law of large numbers.

Date: 2025
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DOI: 10.1080/03610926.2024.2434936

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