On classical and free stable laws

Nizar Demni (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We derive the representative Bernstein measure of the density of some power of a positive stable random variable, as a Fox-H function. Our result makes more explicit that of Biane on the density of its free analog. We also supply analytic arguments explaining the occurence of Kanter's random variable, whose distribution function is the reciprocal function of the density of the Bernstein measure, in both the classical and free settings.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Analyse classique [math.CA]

Nizar Demni. On classical and free stable laws. 2010. ⟨hal-00521017v1⟩