The hitting time of zero for a stable process

Alexey Kuznetsov, Andreas E. Kyprianou, Juan Carlos Pardo, Alexander R. Watson

Research output: Contribution to journalArticle

19 Citations (Scopus)
124 Downloads (Pure)

Abstract

For any two-sided jumping α-stable process, where 1<α<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.
Original languageEnglish
Article number30
Pages (from-to)1-26
JournalElectronic Journal of Probability
Volume19
DOIs
Publication statusPublished - 9 Mar 2014

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