(Non)Differentiability and Asymptotics for Potential Densities of Subordinators

TL;DR

This paper investigates the potential densities of subordinators with positive drift, providing new representations, asymptotic behaviors, and insights into how Levy measure atoms influence smoothness properties.

Contribution

It extends recent results on potential measures and renewal densities for subordinators with positive drift, introducing a Fourier analysis-based representation.

Findings

Derived a new Fourier analysis-based representation of potential densities.

Established asymptotic behaviors of potential densities.

Linked Levy measure atoms to points of (non)smoothness in densities.

Abstract

For subordinators with positive drift we extend recent results on the structure of the potential measures and the renewal densities. Applying Fourier analysis a new representation of the potential densities is derived from which we deduce asymptotic results and show how the atoms of the Levy measure translate into points of (non)smoothness.