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Necessary and sufficient conditions for convergence of first-rare-event-time processes for perturbed semi-Markov processes


Author: D. S. Silvestrov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 95 (2016).
Journal: Theor. Probability and Math. Statist. 95 (2017), 131-151
MSC (2010): Primary 60J10, 60J22, 60J27, 60K15; Secondary 65C40
DOI: https://doi.org/10.1090/tpms/1026
Published electronically: February 28, 2018
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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.


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Additional Information

D. S. Silvestrov
Affiliation: Department of Mathematics, Stockholm University, SE-106 81 Stockholm, Sweden
Email: silvestrov@math.su.se

DOI: https://doi.org/10.1090/tpms/1026
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
Received by editor(s): September 16, 2016
Published electronically: February 28, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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