Explicit identities for Lévy processes associated to symmetric stable processes

M.E. Caballero, J.C. Pardo, and J.L. Pérez

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In this paper, we introduce a new class of Lévy processes which we call hypergeometric-stable Lévy processes because they are obtained from symmetric stable processes through several transformations, where the Gauss hypergeometric function plays an essential role. We characterize the Lévy 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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Bernoulli Volume 17, Number 1 (2011), 34-59.

First available in Project Euclid: 8 February 2011

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first exit time first hitting time Lamperti representation positive self-similar Markov processes symmetric stable Lévy processes


Caballero, M.E.; Pardo, J.C.; Pérez, J.L. Explicit identities for Lévy processes associated to symmetric stable processes. Bernoulli 17 (2011), no. 1, 34--59. doi:10.3150/10-BEJ275.

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