V. S. Korolyuk, N. Limnios, I. V. Samoilenko, “Lévy approximation of impulsive recurrent process with semi-Markov switching”, Theory Stoch. Process., 2010, Volume 16(32), Issue 2,Pages <nobr>77

Lévy approximation of impulsive recurrent process with semi-Markov switching

V. S. Korolyuk^a, N. Limnios^b, I. V. Samoilenko^a

^a Institute of Mathematics, Ukrainian National Academy of Science, Kiev, Ukraine
^b Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, France

Abstract: 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.

Keywords: Lévy approximation, semimartingale, semi-Markov process, impulsive recurrent process, piecewise deterministic Markov process, weak convergence, singular perturbation.

MSC: Primary 60J55, 60B10, 60F17, 60K10; Secondary 60G46, 60G60

Language: English