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Published April 2011 | Submitted
Journal Article Open

A note on diffusion limits of chaotic skew-product flows

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.

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.

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August 19, 2023
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