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The hitting time of zero for a stable process

   
@article{EJP2647,
	author = {Alexey Kuznetsov and Andreas Kyprianou and Juan Carlos Pardo and Alexander Watson},
	title = {The hitting time of zero for a stable process},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {19},
	year = {2014},
	keywords = {Levy processes, stable processes, positive self-similar Markov processes},
	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.},
	pages = {no. 30, 1-26},
	issn = {1083-6489},
	doi = {10.1214/EJP.v19-2647},    
        url = {http://ejp.ejpecp.org/article/view/2647}}