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arXiv · 1101.3087

A Note on Diffusion Limits of Chaotic Skew Product Flows

I. Melbourne·A. M. Stuart
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Abstract

We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation 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 stochastic differential equation 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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I. Melbourne, A. M. Stuart. 2015-04-25. A Note on Diffusion Limits of Chaotic Skew Product Flows. https://doi.org/10.1088/0951-7715%2F24%2F4%2F018

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