Second order subexponential distributions with finite mean and their applications to subordinated distributions

TL;DR

This paper studies the second order tail behavior of subordinated distributions to subexponential distributions with finite mean, introducing the second order subexponential class and enhancing classical tail behavior results.

Contribution

It proposes the second order subexponential distribution class and extends classical tail behavior results without requiring density functions.

Findings

Unified and improved tail behavior results

Characterization of second order subexponential distributions

Applicability to distributions without density functions

Abstract

Consider a probability distribution subordinate to a subexponential distribution with finite mean. In this paper, we discuss the second order tail behavior of the subordinated distribution within a rather general framework in which we do not require the existence of density functions. For this aim, the so-called second order subexponential distribution is proposed and some related properties of its are established. Our results unified and improved some classical results.