NECESSARY AND SUFFICIENT CONDITIONS FOR WEAK CONVERGENCE OF FIRST-RARE-EVENT TIMES FOR SEMI-MARKOV PROCESSES. II
D. S. SILVESTROV AND M. O. DROZDENKOTheory of Stochastic Processes Vol. 12 (28), no. 3–4, 2006, pp. 187–202
Necessary and sufficient conditions for weak convergence of first-rare- event 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.
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