### Lévy Approximation of Impulsive Recurrent Process with Semi-Markov Switching

**V. S. Koroliuk, N. Limnios, I. V. Samoilenko**

*Theory of Stochastic Processes*

*Vol.16 (32), no.2, 2010, pp.77-85*

The weak convergence of an impulsive recurrent process with semi-Markov switching in the scheme of the Lévy approximation is proved. The singular perturbation problem for the compensating operator of an extended Markov renewal process is used to prove the relative compactness.