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The hitting time of zero for a stable process


 
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1. Title Title of document The hitting time of zero for a stable process
 
2. Creator Author's name, affiliation, country Alexey Kuznetsov; York University; Canada
 
2. Creator Author's name, affiliation, country Andreas E Kyprianou; Bath University; United Kingdom
 
2. Creator Author's name, affiliation, country Juan Carlos Pardo; CIMAT; Mexico
 
2. Creator Author's name, affiliation, country Alexander R. Watson; University of Bath; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Levy processes, stable processes, positive self-similar Markov processes
 
3. Subject Subject classification 60G52, 60G18, 60G51
 
4. Description Abstract 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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6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2014-03-09
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2647
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-2647
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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