Unimodality of Hitting Times for Stable Processes

We show that the hitting times for points of real alpha-stable Levy processes (1 < alpha <= 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. (Semin 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.