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Level Crossing Ordering of Skip-Free-to-the-Right Continuous-Time Markov Chains
Published online by Cambridge University Press: 14 July 2016
Abstract
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.
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- © Applied Probability Trust 2005
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