Details

Autor(en) / Beteiligte

• Altaymani, Nuha
• Jedidi, Wissem

Titel

New Monotonicity and Infinite Divisibility Properties for the Mittag-Leffler Function and for Stable Distributions

Ist Teil von

• Mathematics (Basel), 2023-10, Vol.11 (19), p.4141

Ort / Verlag

Basel: MDPI AG

Erscheinungsjahr

2023

Link zum Volltext

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• Hyperbolic complete monotonicity property (HCM) is a way to check if a distribution is a generalized gamma (GGC), hence is infinitely divisible. In this work, we illustrate to which extent the Mittag-Leffler functions Eα,α∈(0,2], enjoy the HCM property, and then intervene deeply in the probabilistic context. We prove that for suitable α and complex numbers z, the real and imaginary part of the functions x↦Eαzx, are tightly linked to the stable distributions and to the generalized Cauchy kernel.