For time-inhomogeneous two-scale SDEs with partially dissipative fast drift, the slow component converges strongly or weakly to an averaged diffusion whose coefficients are built from an evolution system of measures.
Bréhier: The averaging principle for stochastic differential equations driven by a Wiener process revisited, C
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Averaging principles for time-inhomogeneous multi-scale SDEs with partially dissipative coefficients
For time-inhomogeneous two-scale SDEs with partially dissipative fast drift, the slow component converges strongly or weakly to an averaged diffusion whose coefficients are built from an evolution system of measures.