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math.PR2022
Invariant measures of Lévy-type operators and their associated Markov processes
Anita Behme, David Oechsler
A distributional equation as a criterion for invariant measures of Markov processes associated to Lévy-type operators is established. This is obtained via a characterization of inf…
math.PR2021
On -scale functions of spectrally negative Lévy processes
Anita Behme, David Oechsler, René L. Schilling
We obtain series expansions of the -scale functions of arbitrary spectrally negative Lévy processes, including processes with infinite jump activity, and use these to derive var…
math.PR2020
On -scale functions of spectrally negative compound Poisson processes
Anita Behme, David Oechsler
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 r…