Second-order asymptotics for convolution of distributions with light tails

TL;DR

This paper investigates the detailed second-order tail asymptotics of convolutions of distributions with exponential tails, providing precise results under second-order regular variation conditions.

Contribution

It derives the second-order asymptotics for convolutions of light-tailed distributions, advancing understanding of their tail behavior beyond first-order approximations.

Findings

Derived explicit second-order tail asymptotics for convolutions

Established conditions under second-order regular variation

Enhanced accuracy in tail probability estimates

Abstract

In this paper, asymptotic behavior of convolution of distributions belonging to two subclasses of distributions with exponential tails are considered, respectively. The precise second-order tail asymptotics of the convolutions are derived under the condition of second-order regular variation.