Explicit identities for Lévy processes associated to symmetric stable processes

Details Explicit identities for Lévy processes associated to symmetric stable processes Explicit identities for Lévy processes associated to symmetric stable processes

2009-11-03

arxiv.org/abs/0911.0712v1

Mathematics

Probability

Scientific paper

In this paper we introduce a new class of L\'evy processes which we call hypergeometric-stable L\'evy processes, because they are obtained from symmetric stable processes through several transformations and where the Gauss hypergeometric function plays an essential role. We characterize the L\'evy measure of this class and obtain several useful properties such as the Wiener Hopf factorization, the characteristic exponent and some associated exit problems.

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