The Annals of Probability

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

Andreas E. Kyprianou, Juan Carlos Pardo, and Alexander R. Watson

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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.

Article information

Source
Ann. Probab. Volume 42, Number 1 (2014), 398-430.

Dates
First available in Project Euclid: 9 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.aop/1389278528

Digital Object Identifier
doi:10.1214/12-AOP790

Mathematical Reviews number (MathSciNet)
MR3161489

Zentralblatt MATH identifier
1306.60051

Subjects
Primary: 60G52: Stable processes 60G18: Self-similar processes 60G51: Processes with independent increments; Lévy processes

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

Citation

Kyprianou, Andreas E.; Pardo, Juan Carlos; Watson, Alexander R. Hitting distributions of $\alpha$-stable processes via path censoring and self-similarity. Ann. Probab. 42 (2014), no. 1, 398--430. doi:10.1214/12-AOP790. https://projecteuclid.org/euclid.aop/1389278528


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