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L² Diffusion Approximation for Slow Motion in Averaging

Yuri Kifer

Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel

https://doi.org/10.1142/S0219493703000693Cited by:27 (Source: Crossref)

Abstract

Assuming that the fast motion in averaging is sufficiently well mixing we show that the slow motion can be approximated in the L²-sense by a diffusion solving Hasselmann's nonlinear stochastic differential equation and which provides a much better approximation than the one suggested by the averaging principle. Previously, only weak limit theorems in averaging were known which cannot justify, in principle, a nonlinear diffusion approximation of the slow motion.

Keywords:

AMSC: Primary 34C29, Secondary 60F15, Secondary 60J60, Secondary 70K65

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