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Theory of Probability and Mathematical Statistics

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Poisson approximation of processes with locally independent increments and Markov switching


Authors: N. Limnios and I. V. Samoilenko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 89 (2013).
Journal: Theor. Probability and Math. Statist. 89 (2014), 115-126
MSC (2010): Primary 60J55, 60B10, 60F17, 60K10; Secondary 60G46, 60G60
DOI: https://doi.org/10.1090/S0094-9000-2015-00939-X
Published electronically: January 26, 2015
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Abstract: The weak convergence of additive functionals is studied for stochastic processes with locally independent increments and with Markov switching in the scheme of Poisson approximation. The singular perturbation problem for the generator of a Markov process is used to prove the relative compactness.


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Additional Information

N. Limnios
Affiliation: Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, France
Email: nlimnios@dma.utc.fr

I. V. Samoilenko
Affiliation: Institute of Mathematics, Ukrainian National Academy of Science, Kyiv, Ukraine
Email: isamoil@imath.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-2015-00939-X
Keywords: Poisson approximation, semimartingale, Markov process, independent increments, piecewise deterministic Markov process, weak convergence, singular perturbation
Received by editor(s): October 18, 2012
Published electronically: January 26, 2015
Article copyright: © Copyright 2015 American Mathematical Society