A proof of Bondesson’s conjecture on stable densities

Pierre Bosch; Thomas Simon

doi:10.1007/s11512-015-0216-0

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Home > Journals > Ark. Mat. > Volume 54 > Issue 1 > Article

April 2016 A proof of Bondesson’s conjecture on stable densities

Pierre Bosch, Thomas Simon

Author Affiliations +

Pierre Bosch,¹ Thomas Simon²
¹Laboratoire Paul Painlevé, Université Lille 1
²Laboratoire Paul Painlevé, Université Lille 1; Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud

Ark. Mat. 54(1): 31-38 (April 2016). DOI: 10.1007/s11512-015-0216-0

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Abstract

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

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Pierre Bosch. Thomas Simon. "A proof of Bondesson’s conjecture on stable densities." Ark. Mat. 54 (1) 31 - 38, April 2016. https://doi.org/10.1007/s11512-015-0216-0