Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 16 (2011), paper no. 8, 84-95.
A convergent series representation for the density of the supremum of a stable process
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.
Electron. Commun. Probab., Volume 16 (2011), paper no. 8, 84-95.
Accepted: 23 January 2011
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G52: Stable processes
This work is licensed under aCreative Commons Attribution 3.0 License.
Hubalek, Friedrich; Kuznetsov, Alexey. A convergent series representation for the density of the supremum of a stable process. Electron. Commun. Probab. 16 (2011), paper no. 8, 84--95. doi:10.1214/ECP.v16-1601. https://projecteuclid.org/euclid.ecp/1465261964