On free infinite divisibility for classical Meixner distributions

• Autorzy: Bożejko M. , Hasebe T.
• Języki publikacji: EN

Abstrakty

EN

We prove that symmetric Meixner distributions, whose probability densities are proportional to |Γ(t + ix)|², are freely infinitely divisible for 0 < t ≤ 1/2. The case t = 1/2 corresponds to the law of Lévy’s stochastic area whose probability density is 1/cosh(πx). A logistic distribution, whose probability density is proportional to 1/cosh²(πx), is also freely infinitely divisible.

Słowa kluczowe

EN

Meixner distribution; Lévy’s stochastic area; logistic distribution; free infinite divisibility

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2013
• Tom: Vol. 33, Fasc. 2
• Strony: 363--375
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Bożejko M.

• Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Hasebe T.

• Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
• Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 route de Gray, 25030 Besançon cedex, France

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).