Convolutions of long-tailed and subexponential distributions

TL;DR

This paper investigates the properties of convolutions involving long-tailed and subexponential distributions, providing new theoretical results and simplifying existing proofs to enhance understanding of their behavior in stochastic systems.

Contribution

It introduces novel results on convolutions of long-tailed and subexponential distributions with a straightforward approach, clarifying their standard properties.

Findings

New theoretical properties of convolutions established

Simplified proofs of existing properties provided

Enhanced understanding of stochastic system analysis

Abstract

Convolutions of long-tailed and subexponential distributions play a major role in the analysis of many stochastic systems. We study these convolutions, proving some important new results through a simple and coherent approach, and showing also that the standard properties of such convolutions follow as easy consequences.