On $q$-scale functions of spectrally negative compound Poisson processes
Probability
2020-08-03 v1
Abstract
Scale functions play a central role in the fluctuation theory of spectrally negative L\'evy processes. For spectrally negative compound Poisson processes with positive drift, a new representation of the -scale functions in terms of the characteristics of the process is derived. Moreover, similar representations of the derivatives and the primitives of the -scale functions are presented. The obtained formulae for the derivatives allow for a complete exposure of the smoothness properties of the considered -scale functions. Some explicit examples of -scale functions are given for illustration.
Keywords
Cite
@article{arxiv.2007.15880,
title = {On $q$-scale functions of spectrally negative compound Poisson processes},
author = {Anita Behme and David Oechsler},
journal= {arXiv preprint arXiv:2007.15880},
year = {2020}
}