A proof of Bondesson's conjecture on stable densities

Abstract

We show that positive $\alpha$-stable densities are hyperbolically completely monotone if and only if $\alpha \le 1/2$. This gives a positive answer to a question raised by L. Bondesson in 1977.

References in corpus (2)

• Further examples of GGC and HCM densities
• HCM Property and the Half-Cauchy Distribution

Cited by in corpus (6)

• Some properties of the free stable distributions
• Infinitely divisible modified Bessel distributions
• A class of scale mixtures of gamma(k)-distributions that are generalized gamma convolutions
• New monotonicity and infinite divisibility properties for the Mittag-Leffler function and for the stable distributions
• On a moment problem related to Bernstein functions
• Density solutions to a class of integro-differential equations