Intermixing “according to Ibragimov”. Estimate for rate of approach of family of integral functionals of solution of differential equation with periodic coefficients to family of the Wiener processes. Some applications. II - Bondarev, B. V.; Kozyr', S. M. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
In the first part of this work, we obtain estimates for the rate of approach of integrals of a family of "physical" white noises to a family of the Wiener processes. By using this result, we establish an estimate for the rate of approach of a family of solutions of ordinary differential equations, disturbed by some physical white noises, to a family of solutions of the corresponding Ito equations. We consider the case where the coefficient of random disturbance is separated from zero as well as the case where it is not separated from zero.