We show that the hitting times for points of real α-stable Lévy processes (1 < α ≤ 2) are unimodal random variables. The argument relies on strong unimodality and several recent multiplicative identities in law. In the symmetric case we use a factorization of Yano et al. (Sémin Probab XLII:187–227, 2009), whereas in the completely asymmetric case we apply an identity of the second author (Simon, Stochastics 83(2):203–214, 2011). The method extends to the general case thanks to a fractional moment evaluation due to Kuznetsov et al. (Electr. J. Probab. 19:30, 1–26, 2014), for which we also provide a short independent proof.
Hitting time Kanter random variable Self-decomposability Size-bias Stable Lévy process Unimodality
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Ce travail a bénéficié d’une aide de l’Agence Nationale de la Recherche portant la référence ANR-09-BLAN-0084-01.