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A note on diffusion limits of chaotic skew-product flows

Melbourne, I. and Stuart, A. M. (2011) A note on diffusion limits of chaotic skew-product flows. Nonlinearity, 24 (4). pp. 1361-1367. ISSN 0951-7715. doi:10.1088/0951-7715/24/4/018.

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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.

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Additional Information:© 2011 IOP Publishing Ltd. & London Mathematical Society. Received 2 October 2010, in final form 21 February 2011. Published 17 March 2011. The authors are grateful to Niklas Bräannström and Matthew Nicol for helpful discussions. AMS is grateful to EPSRC and ERC for financial support. The research of IM was supported in part by EPSRC Grant EP/F031807/01.
Funding AgencyGrant Number
European Research Council (ERC)UNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)EP/F031807/01
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ85
Issue or Number:4
Classification Code:Mathematics Subject Classification: 37A50, 60H10, 34E13, 60F05, 60F10
Record Number:CaltechAUTHORS:20160804-164518594
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Official Citation:I Melbourne and A M Stuart 2011 Nonlinearity 24 1361
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69455
Deposited By: Linda Taddeo
Deposited On:05 Aug 2016 00:26
Last Modified:11 Nov 2021 04:14

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