Unimodality of hitting times for stable processes

Abstract

We show that the hitting times for points of real $\alpha -$stable Lévy processes ($1<\alpha \le 2$) 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., whereas in the completely asymmetric case we apply an identity of the second author. The method extends to the general case thanks to a fractional moment evaluation due to Kuznetsov et al.