Useful martingales for stochastic storage processes with Lévy-type input

O. Kella, O.J. Boxma

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

In this paper we generalize the martingale of Kella and Whitt to the setting of Lévy-type processes and show that the (local) martingales obtained are in fact square-integrable martingales which upon dividing by the time index converge to zero almost surely and in L^2. The reflected Lévy-type process is considered as an example. Keywords: Lévy-type process; Lévy storage system; Kella-Whitt martingale
Original languageEnglish
Pages (from-to)439-449
JournalJournal of Applied Probability
Volume50
Issue number2
DOIs
Publication statusPublished - 2013

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