Fonctions de Mittag-Leffler et processus de Lévy stables sans saut négatif

Thomas Simon (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

It is noticed that a certain transform of the Mittag-Leffler function Ea is completely monotone for a in [1,2]. Using the explicit expressions of its Bernstein density, an identity in law between suprema of completely asymmetric Levy a-stable processes is obtained. In the spectrally positive case, we retrieve the exact expression of a unilateral small deviation constant which had been previously obtained by a different method by Bernyk, Dalang and Peskir.

Mots clés: Processus de Lévy stable; Factorisation de Wiener-Hopf; Fonction de Mittag-Leffler; Processus de Lévy stable.

Domaines: Probabilités [math.PR]

Thomas Simon. Fonctions de Mittag-Leffler et processus de Lévy stables sans saut négatif. 2009. ⟨hal-00375396⟩