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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 Lévy 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.]
Published: Feb 4, 2011
Keywords: Scale functions; spectrally negative Lévy processes; Mittag-Leffler functions; Wiener-Hopf factorization
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