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

TL;DR

This paper proves that alpha-stable densities are hyperbolically completely monotone for specific ranges of alpha, addressing a problem posed by Bondesson and expanding understanding of their properties.

Contribution

It establishes the hyperbolic complete monotonicity of alpha-stable densities for certain alpha ranges, providing new insights into their structure.

Findings

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

Addresses a problem posed by Bondesson regarding HCM properties.

Expands the class of stable densities known to be HCM.

Abstract

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 $\alpha \in ]0,1/4] \cup [1/3,1/2]$.