On $q$-scale functions of spectrally negative L\'evy processes

Anita Behme; David Oechsler; René L. Schilling

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arXiv · 2109.09359

On $q$-scale functions of spectrally negative L\'evy processes

Anita Behme·David Oechsler·René L. Schilling

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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.

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Anita Behme, David Oechsler, René L. Schilling. 2021-09-20. On $q$-scale functions of spectrally negative L\'evy processes. https://arxiv.org/abs/2109.09359

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