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Necessary and sufficient conditions for convergence of first-rare-event-time processes for perturbed semi-Markov processes. (English) Zbl 1390.60270

Theory Probab. Math. Stat. 95, 131-151 (2017) and Teor. Jmovirn. Mat. Stat. 95, 119-137 (2016).
Summary: Necessary and sufficient conditions for convergence in distribution of first-rare-event times and convergence in Skorokhod J-topology of first-rare-event-time processes for perturbed semi-Markov processes with finite phase space are obtained.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J22 Computational methods in Markov chains
60J27 Continuous-time Markov processes on discrete state spaces
60K15 Markov renewal processes, semi-Markov processes
65C40 Numerical analysis or methods applied to Markov chains
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References:

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