A proof of Bondesson's conjecture on stable densities

TL;DR

This paper proves Bondesson's conjecture by characterizing when positive alpha-stable densities are hyperbolically completely monotone, confirming the conjecture for alpha less than or equal to 1/2.

Contribution

The paper provides a complete proof of Bondesson's conjecture, establishing a precise condition for hyperbolic complete monotonicity of positive alpha-stable densities.

Findings

Positive alpha-stable densities are hyperbolically completely monotone if and only if alpha ≤ 1/2.

Answers a question posed by Bondesson in 1977.

Clarifies the monotonicity properties of 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.