Melbourne, I and Stuart, A. M.. (2011) A note on diffusion limits of chaotic skew-product flows. Nonlinearity, Vol.24 (No.4). pp. 1361-1367. ISSN 0951-7715

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Abstract

We provide an explicit rigorous derivation of a diffusion limit-a stochastic differential equation (SDE) with additive noise-from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a slowly evolving system driven by a fast chaotic flow. Under mild assumptions on the fast flow, we prove convergence to a SDE as the time-scale separation grows. In contrast to existing work, we do not require the flow to have good mixing properties. As a consequence, our results incorporate a large class of fast flows, including the classical Lorenz equations.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Nonlinearity
Publisher:	Institute of Physics Publishing Ltd.
ISSN:	0951-7715
Date:	April 2011
Volume:	Vol.24
Number:	No.4
Page Range:	pp. 1361-1367
Identification Number:	10.1088/0951-7715/24/4/018
Status:	Peer Reviewed
Publication Status:	Published
Funder:	Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC)
Grant number:	EP/F031807/01 (EPSRC)
URI:	http://wrap.warwick.ac.uk/id/eprint/41727

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