Abstract.
In systems which combine fast and slow motions it is usually impossible to study directly corresponding two scale equations and the averaging principle suggests to approximate the slow motion by averaging in fast variables. We consider the averaging setup when both fast and slow motions are diffusion processes depending on each other (fully coupled) and show that there exists a diffusion process which approximates the slow motion in the $L^2$ sense much better than the averaged motion prescribed by the averaging principle.
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The authors are partially supported by INTAS, project No. 99-00559 and by US-Israel BSF, respectively. Part of the work was done during the visit of the 1st author to the Hebrew University.
Mathematics Subject Classification (2000): Primary 34C29; Secondary 60F15, 58J65
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Bakhtin, V., Kifer, Y. Diffusion approximation for slow motion in fully coupled averaging. Probab. Theory Relat. Fields 129, 157–181 (2004). https://doi.org/10.1007/s00440-003-0326-7
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DOI: https://doi.org/10.1007/s00440-003-0326-7