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

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  • Fengxiang Feng
  • Haiwu Huang

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.

Suggested Citation

  • Fengxiang Feng & Haiwu Huang, 2025. "Baum-Katz-type complete and complete moment convergence theorems for the maximal weighted sums under the sub-linear expectations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(16), pages 5191-5209, August.
    • Handle: RePEc:taf:lstaxx:v:54:y:2025:i:16:p:5191-5209
    DOI: 10.1080/03610926.2024.2434936
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