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

Luisa F. Estrada and Michael A. Högele

Statistics & Probability Letters, 2022, vol. 190, issue C

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.

Keywords: Quantitative Borel–Cantelli Lemma; Quantitative VC theorem; Quantitative strong law of large numbers; Exceedance frequency in the Law of the Iterated Logarithm; Large deviations principle (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109636

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