Bounds and approximations for the transient behavior of continuous-time Markov chains. (English) Zbl 1134.60366

Summary: Discretization is a simple, yet powerful tool in obtaining time-dependent probability distribution of continuous-time Markov chains. One of the most commonly used approaches is uniformization. A recent addition to such approaches is an external uniformization technique. In this paper, we briefly review these different approaches, propose some new approaches, and discuss their performances based on theoretical bounds and empirical computational results. A simple method to get lower and upper bounds for first passage time distribution is also proposed.


60J27 Continuous-time Markov processes on discrete state spaces
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