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Heyde’s theorem under the sub-linear expectations

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  • Zhang, Li-Xin

Abstract

Let {Xn;n≥1} be a sequence of independent and identically distributed random variables in a sub-linear expectation space (Ω,ℋ,E) with a capacity V generated by E. The convergence rate of ∑n=1∞V(|∑k=1nXk|>ϵn) as ϵ→0 is studied. Heyde (1975)’s theorem is shown under the sub-linear expectation.

Suggested Citation

  • Zhang, Li-Xin, 2021. "Heyde’s theorem under the sub-linear expectations," Statistics & Probability Letters, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:stapro:v:170:y:2021:i:c:s016771522030290x
    DOI: 10.1016/j.spl.2020.108987
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    References listed on IDEAS

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    1. Shige Peng & Shuzhen Yang & Jianfeng Yao, 2018. "Improving Value-at-Risk prediction under model uncertainty," Papers 1805.03890, arXiv.org, revised Jun 2020.
    2. Chen, Robert, 1978. "A remark on the tail probability of a distribution," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 328-333, June.
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