2000 character limit reached
On $q$-scale functions of spectrally negative Lévy processes (2109.09359v2)
Published 20 Sep 2021 in math.PR
Abstract: We obtain series expansions of the $q$-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 $q$-scale functions. Moreover, we study smoothness properties of the $q$-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.