Useful martingales for stochastic storage processes with leévy-type input

Abstract

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. © 2013 Applied Probability Trust.