On $q$-scale functions of spectrally negative compound Poisson processes

Anita Behme; David Oechsler

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arXiv · 2007.15880

On $q$-scale functions of spectrally negative compound Poisson processes

Anita Behme·David Oechsler

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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 $q$-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.

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Anita Behme, David Oechsler. 2020-07-31. On $q$-scale functions of spectrally negative compound Poisson processes. https://arxiv.org/abs/2007.15880

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