Useful Martingales for Stochastic Storage Processes with Lévy-Type Input

Offer Kella, Onno Boxma

Research output: Contribution to journalArticlepeer-review


In this paper we generalize the martingale of Kella and Whitt to the setting of Leévy-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 L2. The reflected Leévy-type process is considered as an example.

Original languageAmerican English
Pages (from-to)439-449
Number of pages11
JournalJournal of Applied Probability
Issue number2
StatePublished - Jun 2013


  • Kella-whitt martingale
  • Leévy storage system
  • Leévy-type process

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • General Mathematics


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