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Theory of Probability and Mathematical Statistics



Necessary and Sufficient Conditions for Convergence of First-Rare-Event-Time Processes for Perturbed Semi-Markov Processes

D. S. Silvestrov

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Abstract: 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.

Keywords: Semi-Markov process, First-rare-event time, First-rare-event-time process, Convergence in distribution, Convergence in Skorokhod J-topology, Necessary and sufficient conditions

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