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Diffusion approximation of systems with weakly ergodic Markov perturbations. I


Authors: A. Yu. Veretennikov and A. M. Kulik
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 87 (2012).
Journal: Theor. Probability and Math. Statist. 87 (2013), 13-29
MSC (2010): Primary 60H10, 60J10
DOI: https://doi.org/10.1090/S0094-9000-2014-00901-1
Published electronically: March 21, 2014
MathSciNet review: 3241443
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Abstract | References | Similar Articles | Additional Information

Abstract: Diffusion approximation type results are obtained for a system perturbed by a Markov process whose transition probabilities converge to the invariant distribution nonuniformly with respect to the initial value. In general, the mode of convergence is weaker than the total variation convergence.


References [Enhancements On Off] (What's this?)

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Additional Information

A. Yu. Veretennikov
Affiliation: School of Mathematics, University of Leeds, United Kingdom; Institute for Information Transmission Problems, Moscow, Russia
Email: A.Veretennikov@leeds.ac.uk

A. M. Kulik
Affiliation: Institute for Mathematics, National Academy of Science of Ukraine, Kyiv, Ukraine
Email: kulik@imath.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-2014-00901-1
Keywords: Diffusion approximation, corrector, extended potential
Received by editor(s): May 15, 2012
Published electronically: March 21, 2014
Article copyright: © Copyright 2014 American Mathematical Society

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