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.
"Hitting distributions of $\alpha$-stable processes via path censoring and self-similarity." Ann. Probab. 42 (1) 398 - 430, January 2014. https://doi.org/10.1214/12-AOP790