Geodesic
On large deviations in the averaging principle for stochastic differential equations with periodic coefficients.~II
Izvestiya. Mathematics , Tome 39 (1992) no. 1, pp. 677-701

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The logarithmic asymptotic behavior is established for large deviations of the “slow” motion in the averaging principle for stochastic equations in a finite-dimensional Euclidean space. 
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     author = {A. Yu. Veretennikov},
     title = {On large deviations in the averaging principle for stochastic differential equations with periodic {coefficients.~II}},
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A. Yu. Veretennikov. On large deviations in the averaging principle for stochastic differential equations with periodic coefficients.~II. Izvestiya. Mathematics , Tome 39 (1992) no. 1, pp. 677-701. http://geodesic.mathdoc.fr/item/IM2_1992_39_1_a0/