Open Access
May 2011 On extrema of stable processes
Alexey Kuznetsov
Ann. Probab. 39(3): 1027-1060 (May 2011). DOI: 10.1214/10-AOP577


We study the Wiener–Hopf factorization and the distribution of extrema for general stable processes. By connecting the Wiener–Hopf factors with a certain elliptic-like function we are able to obtain many explicit and general results, such as infinite series representations and asymptotic expansions for the density of supremum, explicit expressions for the Wiener–Hopf factors and the Mellin transform of the supremum, quasi-periodicity and functional identities for these functions, finite product representations in some special cases and identities in distribution satisfied by the supremum functional.


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Alexey Kuznetsov. "On extrema of stable processes." Ann. Probab. 39 (3) 1027 - 1060, May 2011.


Published: May 2011
First available in Project Euclid: 16 March 2011

zbMATH: 1218.60037
MathSciNet: MR2789582
Digital Object Identifier: 10.1214/10-AOP577

Primary: 60G52

Keywords: Clausen function , double Gamma function , elliptic functions , Functional equations , Mellin transform , q-Pochhammer symbol , Stable processes , supremum , Wiener–Hopf factorization

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 3 • May 2011
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