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

TL;DR

This paper enhances the Borel-Cantelli Lemma by analyzing higher moments of overlap counts, leading to applications in quantifying mean deviation frequencies in classical probability laws.

Contribution

It introduces a moment-based quantification of the Borel-Cantelli Lemma and applies it to mean deviation frequencies in the Strong Law and Law of the Iterated Logarithm.

Findings

Higher moments of overlap counts are linked to weighted probability summability.

The approach provides new bounds for mean deviation frequencies.

Applications include refined estimates in classical probability limit laws.

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.