The Annals of Probability
- Ann. Probab.
- Volume 39, Number 3 (2011), 1027-1060.
On extrema of stable processes
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.
Ann. Probab., Volume 39, Number 3 (2011), 1027-1060.
First available in Project Euclid: 16 March 2011
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G52: Stable processes
Kuznetsov, Alexey. On extrema of stable processes. Ann. Probab. 39 (2011), no. 3, 1027--1060. doi:10.1214/10-AOP577. https://projecteuclid.org/euclid.aop/1300281731
- Supplementary material: Appendix A: Detailed proofs of some results related to the double gamma function. This supplement material provides detailed computations needed to derive formulas (4.10), (4.11), (7.1), (7.2), (7.5) and to prove Corollary 3 and Theorem 8.