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On some analytical properties of stable densities
Sonia Fourati
L.Bondesson [1] conjectured that the density of a positive -stable distribution is hyperbolically completely monotone (HCM in short) if and only if 1/2. This was prove…
alpha-stable densities are HCM for alpha \in ]0,1/4] and [1/3,1/2]
Sonia Fourati
We investigate the problem raised by L. Bondesson, about the hyperbolic complete monotonicity of -stable densities. We prove that densitites of subordinators of order are HC…
Explicit solutions for the exit problem for a class of Lévy processes. Applications to the pricing of double barrier options
Sonia Fourati
Lewis and Mordecki have computed the Wiener-Hopf factorization of a Lévy process whose restriction on of their Lévy measure has a rational Laplace transform. That all…
Fluctuations of Levy processes and scattering theory
Sonia Fourati
We establish a connection between the scattering inverse problem and the determination of the distribution of the position of the Levy process at the exit time of a bounded interva…
Krein's Theory applied to fluctuations of Lévy processes
Sonia Fourati
We give an interpretation of the bilateral exit problem for Lévy processes via the study of an elementary Markov chain. We exhibit a strong connection between this problem and Krei…