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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

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
Published electronically: March 21, 2014
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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.


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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: http://dx.doi.org/10.1090/S0094-9000-2014-00901-1
PII: S 0094-9000(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