Useful martingales for stochastic storage processes with Lévy-type input and decomposition results

Details Useful martingales for stochastic storage processes with Lévy-type input and decomposition results Useful martingales for stochastic storage processes with Lévy-type input and decomposition results

2011-12-20

arxiv.org/abs/1112.4756v1

Mathematics

Probability

25 pages

Scientific paper

In this paper we generalize the martingale of Kella and Whitt to the setting of L\'evy-type processes and show that under some quite minimal conditions the local martingales are actually $L^2$ martingales which upon dividing by the time index converge to zero a.s. and in $L^2$. We apply these results to generalize known decomposition results for L\'evy queues with secondary jump inputs and queues with server vacations or service interruptions. Special cases are polling systems with either compound Poisson or more general L\'evy inputs.

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