Geodesic
Weak convergence of first-rare-event times for semi-Markov processes II
Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 99-118

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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. 
@article{THSP_2009_15_2_a6,
     author = {Myroslav Drozdenko},
     title = {Weak convergence of first-rare-event times for {semi-Markov} processes {II}},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {99--118},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a6/}
}
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Myroslav Drozdenko. Weak convergence of first-rare-event times for semi-Markov processes II. Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 99-118. http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a6/