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Special, conjugate and complete scale functions for spectrally negative Lévy processes. (English) Zbl 1193.60064
Summary: Following from recent developments in F. Hubalek and A. E. Kyprianou [Old and new examples of scale functions for spectrally negative Lévy processes, (2007; arxiv:0801.0393)], the objective of this paper is to provide further methods for constructing new families of scale functions for spectrally negative Lévy processes which are completely explicit. This is the result of an observation in the aforementioned paper which permits feeding the theory of Bernstein functions directly into the Wiener-Hopf factorization for spectrally negative Lévy processes. Many new, concrete examples of scale functions are offered although the methodology in principle delivers still more explicit examples than those listed.

MSC:
60G51 Processes with independent increments; Lévy processes
60J45 Probabilistic potential theory
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