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Diffusion approximation for slow motion in fully coupled averaging. (English) Zbl 1069.34070
Fast and slow motions are averaged as fully coupled diffusion processes. The authors prove the existence of another diffusion process which \(L^2\)-approximates the slow motion much better than the averaged motion prescribed by the averaging principle.

MSC:
34C29 Averaging method for ordinary differential equations
60F15 Strong limit theorems
58J65 Diffusion processes and stochastic analysis on manifolds
34E13 Multiple scale methods for ordinary differential equations
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