Electronic Journal of Probability
- Electron. J. Probab.
- Volume 10 (2005), paper no. 28, 948-961.
On Lévy processes conditioned to stay positive.
We construct the law of Lévy processes conditioned to stay positive under general hypotheses. We obtain a Williams type path decomposition at the minimum of these processes. This result is then applied to prove the weak convergence of the law of Lévy processes conditioned to stay positive as their initial state tends to 0. We describe an absolute continuity relationship between the limit law and the measure of the excursions away from 0 of the underlying Lévy process reflected at its minimum. Then, when the Lévy process creeps upwards, we study the lower tail at 0 of the law of the height of this excursion.
Electron. J. Probab., Volume 10 (2005), paper no. 28, 948-961.
Accepted: 14 July 2005
First available in Project Euclid: 1 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
Secondary: 60G17: Sample path properties
This work is licensed under aCreative Commons Attribution 3.0 License.
Chaumont, Loïc; Doney, Ronald. On Lévy processes conditioned to stay positive. Electron. J. Probab. 10 (2005), paper no. 28, 948--961. doi:10.1214/EJP.v10-261. https://projecteuclid.org/euclid.ejp/1464816829