Geodesic
L\'{e}vy approximation of impulsive recurrent process with semi-Markov switching
Teoriâ slučajnyh processov, Tome 16 (2010) no. 2, pp. 77-85

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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
Mots-clés : singular perturbation. 
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     author = {V. S. Korolyuk and N. Limnios and I. V. Samoilenko},
     title = {L\'{e}vy approximation of impulsive recurrent process with {semi-Markov} switching},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {77--85},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2010_16_2_a8/}
}
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V. S. Korolyuk; N. Limnios; I. V. Samoilenko. L\'{e}vy approximation of impulsive recurrent process with semi-Markov switching. Teoriâ slučajnyh processov, Tome 16 (2010) no. 2, pp. 77-85. http://geodesic.mathdoc.fr/item/THSP_2010_16_2_a8/