WEAK CONVERGENCE OF FIRST-RARE-EVENT TIMES FOR SEMI-MARKOV PROCESSES II
MYROSLAV DROZDENKOTheory of Stochastic Processes Vol.15 (31), no.2, 2009, pp.99-118
Necessary and sufficient conditions for the weak convergence of °ows 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.