On First Passage Times in Discrete Skeletons and Uniformized Versions of a Continuous-Time Markov Chain

Abstract

In this paper, the aim is to study similarities and differences between a continuous-time Markov chain and its uniformized Markov chains and discrete skeletons in terms of first passage times when the taboo subset of states is assumed to be accessible from a class of communicating states. Under the assumption of a finite communicating class, we characterize the first-passage times in terms of either continuous or discrete phase-type random variables. For illustrative purposes, we show how first passage times in uniformized Markov chains and discrete skeletons can be used to approximate the random duration of an outbreak in the SIS epidemic model.