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Zbl 1194.33022
Simon, Thomas
Mittag-Leffler functions and stable Lévy processes without negative jumps. (Fonctions de Mittag-Leffler et processus de Lévy stables sans sauts négatifs.) (French. English summary)
[J] Expo. Math. 28, No. 3, 290-298 (2010). ISSN 0723-0869

Summary: We remark that a certain transformation of the Mittag-Leffler function $\alpha $ is completely monotone for every $\alpha \in [1,2]$. Thanks to the exact expression of its Bernstein density function, we obtain an identity in law between one-sided exit times for completely asymmetric stable Lévy processes. In the spectrally positive case, this identity gives an expression for the density of the running supremum which is different from the one recently obtained by {\it V. Bernyk, R. C. Dalang} and {\it G. Peskir} [Ann. Probab. 36, No.~5, 1777--1789 (2008; Zbl 1185.60051)].

MSC 2000:: *33E12 Mittag-Leffler functions and generalizations
60E05 General theory of probability distributions
60G52 Stable processes

Keywords: Mittag-Leffler function; Lévy processes; Wiener-Hopf factorization

Citations: Zbl 1185.60051

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