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A convergent series representation for the density of the supremum of a stable process

   
@article{ECP1601,
	author = {Friedrich Hubalek and Alexey Kuznetsov},
	title = {A convergent series representation for the density of the supremum of a stable process},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {16},
	year = {2011},
	keywords = {stable processes, supremum, Mellin transform, double Gamma function, Liouville numbers, continued fractions},
	abstract = {We study the density of the supremum of a strictly stable Levy process. We prove that  for almost all values of the index $\alpha$ - except for a dense set of Lebesgue measure zero - the asymptotic series which were obtained  in Kuznetsov (2010) "On extrema of stable processes" are in fact absolutely convergent series representations for the density of the supremum.},
	pages = {no. 8, 84-95},
	issn = {1083-589X},
	doi = {10.1214/ECP.v16-1601},    
        url = {http://ecp.ejpecp.org/article/view/1601}}