TY - JOUR
T1 - The hitting time of zero for a stable process
AU - Kuznetsov, Alexey
AU - Kyprianou, Andreas E.
AU - Pardo, Juan Carlos
AU - Watson, Alexander R.
PY - 2014/3/9
Y1 - 2014/3/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84897826951&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1214/EJP.v19-2647
U2 - 10.1214/EJP.v19-2647
DO - 10.1214/EJP.v19-2647
M3 - Article
AN - SCOPUS:84897826951
SN - 1083-6489
VL - 19
SP - 1
EP - 26
JO - Electronic Journal of Probability
JF - Electronic Journal of Probability
M1 - 30
ER -