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Theory of Stochastic Processes, 2010, Volume 16(32), Issue 2, Pages 77–85 (Mi thsp77)  
Lévy approximation of impulsive recurrent process with semi-Markov switching

V. S. Korolyuka, N. Limniosb, I. V. Samoilenkoa

a Institute of Mathematics, Ukrainian National Academy of Science, Kiev, Ukraine
b Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, France
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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.
Funding agency Grant number
Deutsche Forschungsgemeinschaft 436 UKR 113/94/07-09
The authors thank University of Bielefeld for the hospitality and the financial support by DFG project 436 UKR 113/94/07-09.
Bibliographic databases:
Document Type: Article
MSC: Primary 60J55, 60B10, 60F17, 60K10; Secondary 60G46, 60G60
Language: English
Citation: V. S. Korolyuk, N. Limnios, I. V. Samoilenko, “Lévy approximation of impulsive recurrent process with semi-Markov switching”, Theory Stoch. Process., 16(32):2 (2010), 77–85
Citation in format AMSBIB
\Bibitem{KorLimSam10}
\by V.~S.~Korolyuk, N.~Limnios, I.~V.~Samoilenko
\paper L\'{e}vy approximation of impulsive recurrent process with semi-Markov switching
\jour Theory Stoch. Process.
\yr 2010
\vol 16(32)
\issue 2
\pages 77--85
\mathnet{http://mi.mathnet.ru/thsp77}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2777903}
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