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

@inproceedings{Behme2020OnF, title={On \$q\$-scale functions of spectrally negative compound Poisson processes}, author={Anita Behme and David Oechsler}, year={2020} }

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… CONTINUE READING

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