Hitting distributions of $\alpha$-stable processes via path censoring and self-similarity

Abstract

We consider two first passage problems for stable processes, not necessarily symmetric, in one dimension. We make use of a novel method of path censoring in order to deduce explicit formulas for hitting probabilities, hitting distributions and a killed potential measure. To do this, we describe in full detail the Wiener–Hopf factorization of a new Lamperti-stable-type Lévy process obtained via the Lamperti transform, in the style of recent work in this area.