Useful martingales for stochastic storage processes with Lévy-type input

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 a.s. and in $L^2$. The reflected Lévy-type process is considered as an example.

15 pages. arXiv admin note: substantial text overlap with arXiv:1112.4756