On $q$-scale functions of spectrally negative L\'evy processes
Probability
2022-03-08 v2
Abstract
We obtain series expansions of the -scale functions of arbitrary spectrally negative L\'evy processes, including processes with infinite jump activity, and use these to derive various new examples of explicit -scale functions. Moreover, we study smoothness properties of the -scale functions of spectrally negative L\'evy processes with infinite jump activity. This complements previous results of Chan et al. [7] for spectrally negative L\'evy processes with Gaussian component or bounded variation.
Keywords
Cite
@article{arxiv.2109.09359,
title = {On $q$-scale functions of spectrally negative L\'evy processes},
author = {Anita Behme and David Oechsler and René L. Schilling},
journal= {arXiv preprint arXiv:2109.09359},
year = {2022}
}