Level crossing ordering of skip-free to the right continuous time Markov chains.

Journal of Applied Probability, 42(1) (2005), 52-60
http://www.jstor.org/discover/10.2307/30040769?uid=3738880&uid=2&uid=4&sid=21105101422333

As proposed by Irle and Gani in 2001, a process X is said to be slower in level crossing than a process Y if it takes X stochastically longer to exceed any given level than it does Y. In this paper, we extend a result of Irle (2003), relative to the level crossing ordering of uniformizable skip-free-to-the-right continuous-time Markov chains, to derive a new set of sufficient conditions for the level crossing ordering of these processes. We apply our findings to birth-death processes with and without catastrophes, and M/M/s/c systems.