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.