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Moment estimates in the first Borel–Cantelli Lemma with applications to mean deviation frequencies

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  • Estrada, Luisa F.
  • Högele, Michael A.

Abstract

We quantify the elementary Borel–Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mean deviation frequencies in the Strong Law and the Law of the Iterated Logarithm.

Suggested Citation

  • Estrada, Luisa F. & Högele, Michael A., 2022. "Moment estimates in the first Borel–Cantelli Lemma with applications to mean deviation frequencies," Statistics & Probability Letters, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:stapro:v:190:y:2022:i:c:s0167715222001663
    DOI: 10.1016/j.spl.2022.109636
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    References listed on IDEAS

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    1. Xie, Yuquan, 2009. "A bilateral inequality on a nonnegative bounded random sequence," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1577-1580, July.
    2. Hu, Shuhe & Wang, Xuejun & Li, Xiaoqin & Zhang, Yuanyuan, 2009. "Comments on the paper: A bilateral inequality on the Borel-Cantelli Lemma," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 889-893, April.
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