OLD AND NEW EXAMPLES OF SCALE FUNCTIONS FOR SPECTRALLY Negative Lévy Processes

OLD AND NEW EXAMPLES OF SCALE FUNCTIONS FOR SPECTRALLY Negative Lévy Processes (2009)

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by F. Hubalek , A. E. Kyprianou

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10 - 7 self

BibTeX

@MISC{Hubalek09oldand,
    author = {F. Hubalek and A. E. Kyprianou},
    title = { OLD AND NEW EXAMPLES OF SCALE FUNCTIONS FOR SPECTRALLY Negative Lévy Processes},
    year = {2009}
}

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Abstract

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.

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