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


 
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1. Title Title of document A convergent series representation for the density of the supremum of a stable process
 
2. Creator Author's name, affiliation, country Friedrich Hubalek; Vienna University of Technology
 
2. Creator Author's name, affiliation, country Alexey Kuznetsov; York University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) stable processes, supremum, Mellin transform, double Gamma function, Liouville numbers, continued fractions
 
3. Subject Subject classification 60G52
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Natural Sciences and Engineering Research Council of Canada
 
7. Date (YYYY-MM-DD) 2011-01-23
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1601
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1601
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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