A note on diffusion limits of chaotic skew-product flows
Melbourne, Ian and Stuart, A. M.. (2011) A note on diffusion limits of chaotic skew-product flows. Nonlinearity, Volume 24 (Number 4). pp. 1361-1367. ISSN 0951-7715Full text not available from this repository.
Official URL: http://dx.doi.org/10.1088/0951-7715/24/4/018
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|
|Library of Congress Subject Headings (LCSH):||Stochastic differential equations, Flows (Differentiable dynamical systems)|
|Journal or Publication Title:||Nonlinearity|
|Publisher:||Institute of Physics Publishing Ltd.|
|Official Date:||April 2011|
|Page Range:||pp. 1361-1367|
|Funder:||Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC)|
|Grant number:||EP/F031807/01 (EPSRC)|
 Billingsley P 1999Convergence of Probability Measures(Wiley Series in Probability and Statistics: Probability
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