In the first part of the present paper, we established estimates for the rate of approach of the integrals of a family of “physical” white noises to a family of Wiener processes. We use this result to establish the estimate for the rate of approach of a family of solutions of ordinary differential equations perturbed by some “physical” white noises to a family of solutions of the corresponding Itô equations. We consider both the case where the coefficient of random perturbation is separated from zero and the case where it is not separated from zero.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 3, pp. 303–318, March, 2011.
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Bondarev, B.V., Kozyr’, S.M. Mixing “in the sense of ibragimov.” Estimate for the rate of approach of a family of integral functionals of a solution of a differential equation with periodic coefficients to a family of wiener processes. Some applications. II. Ukr Math J 63, 351–368 (2011). https://doi.org/10.1007/s11253-011-0508-x
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DOI: https://doi.org/10.1007/s11253-011-0508-x