Old and new examples of scale functions for spectrally negative Levy processes

Details Old and new examples of scale functions for spectrally negative Levy processes Old and new examples of scale functions for spectrally negative Levy processes

2007-12-29

arxiv.org/abs/0801.0393v2

Mathematics

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We give a review of the state of the art with regard to the theory of scale functions for spectrally negative Levy processes. From this we introduce a general method for generating new families of scale functions. Using this method we introduce a new family of scale functions belonging to the Gaussian Tempered Stable Convolution (GTSC) class. We give particular emphasis to special cases as well as cross-referencing their analytical behaviour against known general considerations.

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