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Teor. Veroyatnost. i Primenen., 2004, Volume 49, Issue 4, Pages 726–742 (Mi tvp191)  

This article is cited in 5 scientific papers (total in 5 papers)

Poisson approximation of increment processes with Markov switching

V. S. Korolyuka, N. Limniosb

a National Taras Shevchenko University of Kyiv
b Université de Technologie de Compiégne

Abstract: In this paper we present weak convergence results for Markov switched increment processes toward a compound Poisson process. The switching Markov process is considered also with an asymptotic split phase space. These results are obtained by a semimartingale approach.

Keywords: increment process, semimartingale, Markov process, weak convergence, compound Poisson process, merging scheme.

DOI: https://doi.org/10.4213/tvp191

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English version:
Theory of Probability and its Applications, 2005, 49:4, 629–644

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Received: 22.12.2000
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Citation: V. S. Korolyuk, N. Limnios, “Poisson approximation of increment processes with Markov switching”, Teor. Veroyatnost. i Primenen., 49:4 (2004), 726–742; Theory Probab. Appl., 49:4 (2005), 629–644

Citation in format AMSBIB
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\by V.~S.~Korolyuk, N.~Limnios
\paper Poisson approximation of increment processes with
Markov switching
\jour Teor. Veroyatnost. i Primenen.
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\vol 49
\issue 4
\pages 726--742
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\crossref{https://doi.org/10.4213/tvp191}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2142564}
\zmath{https://zbmath.org/?q=an:1090.60073}
\transl
\jour Theory Probab. Appl.
\yr 2005
\vol 49
\issue 4
\pages 629--644
\crossref{https://doi.org/10.1137/S0040585X97981330}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. S. Koroliuk, N. Limnios, “Poisson approximation of processes with locally independent increments with Markov switching”, Theory Stoch. Process., 15(31):1 (2009), 40–48  mathnet  mathscinet  zmath
    2. Koroliuk V.S., Limnios N., “Reliability of Semi-Markov Systems with Asymptotic Merging Phase Space”, Mathematical and Statistical Models and Methods in Reliability: Applications To Medicine, Finance, and Quality Control, Statistics for Industry and Technology, 2010, 3–18  mathscinet  isi
    3. Koroliuk V.S., Limnios N., Samoilenko I.V., “Poisson Approximation of Impulsive Recurrent Process with Semi-Markov Switching”, Stoch Anal Appl, 29:5 (2011), 769–778  crossref  mathscinet  zmath  isi  scopus
    4. Koroliuk V.S., “Bv Gnedenko: Classic of Limit Theorems in the Theory of Probability”, Methodol. Comput. Appl. Probab., 17:1 (2015), 5–14  crossref  mathscinet  zmath  isi  scopus
    5. Koroliuk V.S., Limnios N., Samoilenko I.V., “Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach”, C. R. Math., 354:7 (2016), 723–728  crossref  mathscinet  zmath  isi  elib  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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