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2 results

  • Useful martingales for stochastic storage processes with Lévy input

  • Part of
  • Offer Kella, Ward Whitt
  • Journal:
    Journal of Applied Probability / Volume 29 / Issue 2 / June 1992
    Published online by Cambridge University Press:
    14 July 2016, pp. 396-403
    Print publication:
    June 1992

  • We apply the general theory of stochastic integration to identify a martingale associated with a Lévy process modified by the addition of a secondary process of bounded variation on every finite interval. This martingale can be applied to queues and related stochastic storage models driven by a Lévy process. For example, we have applied this martingale to derive the (non-product-form) steady-state distribution of a two-node tandem storage network with Lévy input and deterministic linear fluid flow out of the nodes.