Necessary and Sufficient Conditions for Convergence of First-Rare-Event   Times for Perturbed Semi-Markov Processes
  Necessary and sufficient conditions for convergence in distribution of first-rare-event times and convergence in Skorokhod J-topology of first-rare-event-time processes for perturbed semi-Markov processes with finite phase space are obtained. 
Dmitrii Silvestrov
math.PR