Open Access
January 2014 Hitting distributions of $\alpha$-stable processes via path censoring and self-similarity
Andreas E. Kyprianou, Juan Carlos Pardo, Alexander R. Watson
Ann. Probab. 42(1): 398-430 (January 2014). DOI: 10.1214/12-AOP790


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.


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Andreas E. Kyprianou. Juan Carlos Pardo. Alexander R. Watson. "Hitting distributions of $\alpha$-stable processes via path censoring and self-similarity." Ann. Probab. 42 (1) 398 - 430, January 2014.


Published: January 2014
First available in Project Euclid: 9 January 2014

zbMATH: 1306.60051
MathSciNet: MR3161489
Digital Object Identifier: 10.1214/12-AOP790

Primary: 60G18 , 60G51 , 60G52

Keywords: hitting distributions , hitting probabilities , hypergeometric Lévy processes , killed potential , Lamperti transform , Lamperti-stable processes , Lévy processes , positive self-similar Markov processes , Stable processes , stable processes conditioned to stay positive

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 1 • January 2014
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