Necessary and sufficient conditions for weak convergence of first-rare-event times for semi-Markov processes. I - Silvestrov, D.S.; Drozdenko, M.O. (Інститут математики НАН України, 2006)
Necessary and sufficient conditions for weak convergence of ﬁrst-rareevent times for semi-Markov processes with ﬁnite set of states are obtained. These results are applied to risk processes and give necessary and sufficient conditions for stable approximation of ruin probabilities including the case of diffusion approximation.