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A note on diffusion limits of chaotic skewproduct flows
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Melbourne, Ian and Stuart, A. M.. (2011) A note on diffusion limits of chaotic skewproduct flows. Nonlinearity, Volume 24 (Number 4). pp. 13611367. ISSN 09517715
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Official URL: http://dx.doi.org/10.1088/09517715/24/4/018
Abstract
We provide an explicit rigorous derivation of a diffusion limita stochastic differential equation (SDE) with additive noisefrom a deterministic skewproduct flow. This flow is assumed to exhibit timescale 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 timescale 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.  
ISSN:  09517715  
Official Date:  April 2011  
Dates: 


Volume:  Volume 24  
Number:  Number 4  
Page Range:  pp. 13611367  
Identifier:  10.1088/09517715/24/4/018  
Status:  Peer Reviewed  
Publication Status:  Published  
Funder:  Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC)  
Grant number:  EP/F031807/01 (EPSRC)  
References:  [1] Billingsley P 1999Convergence of Probability Measures(Wiley Series in Probability and Statistics: Probability 

URI:  http://wrap.warwick.ac.uk/id/eprint/41727 
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