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Explicit identities for Lévy processes associated to symmetric stable processes

In this paper we introduce a new class of Levy processes which we call hypergeometric- stable Levy 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 Levy measure of this class and obtain several useful properties such as the Wiener Hopf factorization, the characteristic exponent and some associated exit problems.