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2014 The hitting time of zero for a stable process
Alexey Kuznetsov, Andreas Kyprianou, Juan Carlos Pardo, Alexander Watson
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Electron. J. Probab. 19: 1-26 (2014). DOI: 10.1214/EJP.v19-2647


For any two-sided jumping $\alpha$-stable process, where $1 < \alpha<2$, we find an explicit identity for the law of the first hitting time of the origin. This complements existing work in the symmetric case and the spectrally one-sided case; cf. Yano-Yano-Yor (2009) and Cordero (2010), and Peskir (2008) respectively. We appeal to the Lamperti-Kiu representation of Chaumont-Panti-Rivero (2011) for real-valued self similar Markov processes. Our main result follows by considering a vector-valued functional equation for the Mellin transform of the integrated exponential Markov additive process in the Lamperti-Kiu representation. We conclude our presentation with some applications.


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Alexey Kuznetsov. Andreas Kyprianou. Juan Carlos Pardo. Alexander Watson. "The hitting time of zero for a stable process." Electron. J. Probab. 19 1 - 26, 2014.


Accepted: 9 March 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1293.60055
MathSciNet: MR3183574
Digital Object Identifier: 10.1214/EJP.v19-2647

Primary: 60G52
Secondary: 60G18 , 60G51

Keywords: Levy processes , positive self-similar Markov processes , Stable processes


Vol.19 • 2014
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