Bernoulli

Explicit identities for Lévy processes associated to symmetric stable processes

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

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Abstract

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.

Article information

Source
Bernoulli Volume 17, Number 1 (2011), 34-59.

Dates
First available in Project Euclid: 8 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.bj/1297173832

Digital Object Identifier
doi:10.3150/10-BEJ275

Mathematical Reviews number (MathSciNet)
MR2797981

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

Citation

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. https://projecteuclid.org/euclid.bj/1297173832


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