Poisson approximation of processes with locally independent increments and Markov switching
Authors:
N. Limnios and I. V. Samoilenko
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
MathSciNet review:
3235179
Full-text PDF Free Access
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Additional Information
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.
References
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References
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- J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin, 1987. MR 959133 (89k:60044)
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- V. S. Koroliuk, N. Limnios, and I. V. Samoilenko, Poisson approximation of processes with locally independent increments with Markov switching, Theory Stoch. Process. 15(31) (2009), no. 1, 40–48; corrections in Letter from the publishers, Theory Stoch. Process. 15(31) (2009), no. 2, 164. MR 2598522 (2010m:60112)
- H. J. Kushner, Weak Convergence Methods and Singular Perturbed Stochastic Control and Filtering Problems, Birkhäuser, Boston, 1990. MR 1102242 (92d:93003)
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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
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
