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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. II


Authors: A. Yu. Veretennikov and A. M. Kulik
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 88 (2013).
Journal: Theor. Probability and Math. Statist. 88 (2014), 1-17
MSC (2010): Primary 60H10, 60J10
Published electronically: July 24, 2014
MathSciNet review: 3112631
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Abstract: This paper is a continuation of the paper [A. Yu. Veretennikov and A. M. Kulik, Diffusion approximation for systems with weakly ergodic Markov perturbations. I, Theory Probab. Math. Statist.87 (2012), 13-29]. Some corollaries of the general results are given in several particular cases being of their own interest. An example of a process being a solution of a stochastic differential equation with a Lévy noise is considered; we show that the assumptions imposed on the process can effectively be verified.


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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 of Mathematics, National Academy of Science, Tereschenkivs’ka Street, 3,\lb01601, Kyiv, Ukraine
Email: kulik@imath.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2014-00915-1
PII: S 0094-9000(2014)00915-1
Keywords: Diffusion approximation, distance in variation, Kantorovich--Rubinstein distance, central limit theorem
Received by editor(s): May 15, 2012
Published electronically: July 24, 2014
Article copyright: © Copyright 2014 American Mathematical Society