On $q$scale functions of spectrally negative compound Poisson processes
Abstract
Scale functions play a central role in the fluctuation theory of spectrally negative Lévy processes. For spectrally negative compound Poisson processes with positive drift, a new representation of the $q$scale functions in terms of the characteristics of the process is derived. Moreover, similar representations of the derivatives and the primitives of the $q$scale functions are presented. The obtained formulae for the derivatives allow for a complete exposure of the smoothness properties of the considered $q$scale functions. Some explicit examples of $q$scale functions are given for illustration.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2007.15880
 Bibcode:
 2020arXiv200715880B
 Keywords:

 Mathematics  Probability