Useful martingales for stochastic storage processes with Lévy input
- 1 June 1992
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 29 (2) , 396-403
- https://doi.org/10.2307/3214576
Abstract
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.Keywords
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