Structural properties of reflected Lévy processes

L.N. Andersen, M.R.H. Mandjes

Research output: Contribution to journalArticleAcademicpeer-review

11 Citations (Scopus)

Abstract

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 Vt being the position of the reflected process at time t , we focus on the analysis of ¿(t) := EVt and ¿(t) := VarVt . We prove that for the one- and two-sided reflection, ¿(t) is increasing and concave, whereas for the onesided reflection, ¿(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.
Original languageEnglish
Pages (from-to)301-322
JournalQueueing Systems: Theory and Applications
Volume63
Issue number1-4
DOIs
Publication statusPublished - 2009

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