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Theory of Stochastic Processes, 2009, Volume 15(31), Issue 2, Pages 99–118 (Mi thsp88)  
Weak convergence of first-rare-event times for semi-Markov processes II

Myroslav Drozdenko

Division of Mathematics and Applied Mathematics, Mälardalen University, Box 883, SE-72123 Västerås, Sweden
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Abstract: Necessary and sufficient conditions for the weak convergence of flows of rare events controlled by semi-Markov processes with a finite set of states in schemes of series are given. Applications of the obtained results to geometric sums, risk processes, and queueing systems are presented.
Keywords: Weak convergence, semi-Markov processes, first-rare-event times, limit theorems, necessary and sufficient conditions, flows of rare events, risk theory, queueing systems.
Bibliographic databases:
Document Type: Article
MSC: 60K15, 60F17, 60K20
Language: English
Citation: Myroslav Drozdenko, “Weak convergence of first-rare-event times for semi-Markov processes II”, Theory Stoch. Process., 15(31):2 (2009), 99–118
Citation in format AMSBIB
\Bibitem{Dro09}
\by Myroslav Drozdenko
\paper Weak convergence of first-rare-event times for semi-Markov processes II
\jour Theory Stoch. Process.
\yr 2009
\vol 15(31)
\issue 2
\pages 99--118
\mathnet{http://mi.mathnet.ru/thsp88}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2598530}
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