Exponential tail estimates in the Law of Ordinary Logarithm (LOL) for arrays of random variables

TL;DR

This paper develops exponential tail bounds for normalized sums of arrays of random variables under the ordinary logarithm, extending classical results to dependent variables.

Contribution

It introduces exponential tail estimates for sums of dependent random variables normalized by the ordinary logarithm, broadening the scope of the Law of Ordinary Logarithm.

Findings

Derived exponential tail bounds for normalized sums

Applicable to dependent random variables

Extends classical LOL results

Abstract

We derive exponential bounds for tail of distribution for natural, i.e. under ordinary logarithm, normalized sums of arrays of random variables, not necessarily independent.