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

D. S. SILVESTROV AND M. O. DROZDENKO


Theory of Stochastic Processes Vol. 12 (28), no. 3–4, 2006, pp. 151–186

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.

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