(Non)Differentiability and Asymptotics for Potential Densities of Subordinators

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.

27 pages, appeared in Electronic Journal of Probability 2011