Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 15 (2010), paper no. 51, 572-584.
Right inverses of Levy processes: the excursion measure in the general case
This article is about right inverses of Lévy processes as first introduced by Evans in the symmetric case and later studied systematically by the present authors and their co-authors. Here we add to the existing fluctuation theory an explicit description of the excursion measure away from the (minimal) right inverse. This description unifies known formulas in the case of a positive Gaussian coefficient and in the bounded variation case. While these known formulas relate to excursions away from a point starting negative continuously, and excursions started by a jump, the present description is in terms of excursions away from the supremum continued up to a return time. In the unbounded variation case with zero Gaussian coefficient previously excluded, excursions start negative continuously, but the excursion measures away from the right inverse and away from a point are mutually singular. We also provide a new construction and a new formula for the Laplace exponent of the minimal right inverse.
Electron. Commun. Probab., Volume 15 (2010), paper no. 51, 572-584.
Accepted: 12 December 2010
First available in Project Euclid: 6 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G51: Processes with independent increments; Lévy processes
This work is licensed under aCreative Commons Attribution 3.0 License.
Savov, Mladen; Winkel, Matthias. Right inverses of Levy processes: the excursion measure in the general case. Electron. Commun. Probab. 15 (2010), paper no. 51, 572--584. doi:10.1214/ECP.v15-1590. https://projecteuclid.org/euclid.ecp/1465243994