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Baum–Katz-type complete and complete moment convergence theorems for the maximum of partial sums under sub-linear expectations

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  • Feng, Fengxiang

Abstract

Let {X,Xn;n≥0} be a sequence of independent and identically distributed random variables in a sub-linear expectation space (Ω,H,Ê). We establish Baum–Katz-type complete and complete moment convergence theorems for the maximum of partial sums in a sub-linear expectation space. Our results extend the corresponding complete convergence results of probability spaces to sub-linear expectation spaces.

Suggested Citation

  • Feng, Fengxiang, 2023. "Baum–Katz-type complete and complete moment convergence theorems for the maximum of partial sums under sub-linear expectations," Statistics & Probability Letters, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:stapro:v:197:y:2023:i:c:s0167715223000421
    DOI: 10.1016/j.spl.2023.109818
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    References listed on IDEAS

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    1. Feng-Xiang Feng & Ding-Cheng Wang & Qun-Ying Wu, 2019. "Complete convergence for weighted sums of negatively dependent random variables under the sub-linear expectations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(6), pages 1351-1366, March.
    2. Magda Peligrad & Allan Gut, 1999. "Almost-Sure Results for a Class of Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 12(1), pages 87-104, January.
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