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Poisson Approximation of Impulsive Recurrent Process with Semi-Markov Switching |
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| Authors: | V. S. Koroliuk I. V. Samoilenko |
| Affiliation: | Institute of Mathematics , Ukrainian National Academy of Science , Kiev , Ukraine |
| Abstract: | In this article, the weak convergence of impulsive recurrent process with semi-Markov switching in the scheme of Poisson approximation is proved. Singular perturbation problem for the compensating operator of the extended Markov renewal process is used to prove the relative compactness. |
| Keywords: | Impulsive recurrent process Insurance Poisson approximation Semimartingale Semi-Markov process Risk process Singular perturbation Weak convergence |