- Structural properties of reflected Lévy processes
- Queueing Systems
- Volume | Issue number
- 63 | 1-4
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
This paper considers a number of structural properties of reflected Lévy processes, where both one-sided reflection (at 0) and two-sided reflection (at both 0 and K > 0) are examined. With V-t being the position of the reflected process at time t, we focus on the analysis of zeta(t) := EVt and xi(t) := Var V-t. We prove that for the one- and two-sided reflection, zeta(t) is increasing and concave, whereas for the one-sided reflection, xi(t) is increasing. In most proofs we first establish the claim for the discrete-time counterpart (that is, a reflected random walk), and then use a limiting argument. A key step in our proofs for the two-sided reflection is a new representation of the position of the reflected process in terms of the driving Lévy process.
- go to publisher's site
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.