The Annals of Probability
- Ann. Probab.
- Volume 42, Number 1 (2014), 398-430.
Hitting distributions of $\alpha$-stable processes via path censoring and self-similarity
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.
Ann. Probab. Volume 42, Number 1 (2014), 398-430.
First available in Project Euclid: 9 January 2014
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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
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