NECESSARY AND SUFFICIENT CONDITIONS FOR WEAK CONVERGENCE OF FIRST-RARE-EVENT TIMES FOR SEMI-MARKOV PROCESSES. II

D. S. SILVESTROV AND M. O. DROZDENKO

Theory 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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