alpha-stable densities are HCM for alpha \in ]0,1/4] and [1/3,1/2].

Sonia Fourati (1, 2)

1 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We investigate the problem raised by L. Bondesson, about the hyperbolic complete monotonicity of $\alpha$-stable densities. We prove that densitites of subordinators of order $\alpha$ are HCM for $\alpha \in ]0,1/4] \cup [1/3,1/2]$.

Mots clés: stable desnities; hyperbolic completely monotone functions. Riemann-Hilbert problem

Domaines: Probabilités [math.PR]

Sonia Fourati. alpha-stable densities are HCM for alpha \in ]0,1/4] and [1/3,1/2].. 2013. ⟨hal-00859346⟩