We prove that a sufficient condition for stochastic Ito systems to be exponentially dichotomous on the semiaxis is that the nonhomogeneous system has mean square bounded solutions.
The averaging method on the semi-axis is justified for systems of difference equations. A theorem on closeness of the corresponding solutions of the exact and averaged systems on the semi-axis is proved. This theorem is analogous to N. N. Bogoliubov's second theorem about an averaging method for systems of difference equations.
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