Necessary and sufficient conditions for weak convergence of first-rare-event times for semi-Markov processes. II

Abstract

Necessary and suffcient conditions for weak convergence of first-rareevent times for semi-Markov processes, obtained in the first part of this paper [66], are applied to counting processes generating by flows of rare events controlled by semi-Markov processes, random geometric sums, and risk processes. In particular, necessary and sufficient conditions for stable approximation of ruin probabilities including the case of diffusion approximation are given.