Useful martingales for stochastic storage processes with L\'{e}vy-type input
Probability
2017-11-22 v1
Abstract
In this paper we generalize the martingale of Kella and Whitt to the setting of L\'{e}vy-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 . The reflected L\'{e}vy-type process is considered as an example.
Keywords
Cite
@article{arxiv.1210.2209,
title = {Useful martingales for stochastic storage processes with L\'{e}vy-type input},
author = {Offer Kella and Onno Boxma},
journal= {arXiv preprint arXiv:1210.2209},
year = {2017}
}
Comments
15 pages. arXiv admin note: substantial text overlap with arXiv:1112.4756