Diffusion approximation of systems with weakly ergodic Markov perturbations. II

Veretennikov, A.; Kulik, A.

doi:10.1090/S0094-9000-2014-00915-1

Diffusion approximation of systems with weakly ergodic Markov perturbations. II

Authors: A. Yu. Veretennikov and A. M. Kulik
Translated by: N. Semenov
Journal: Theor. Probability and Math. Statist. 88 (2014), 1-17
MSC (2010): Primary 60H10, 60J10
DOI: https://doi.org/10.1090/S0094-9000-2014-00915-1
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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