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. doi:10.1088/0951-7715/24/4/018 ISSN 0951-7715.

Research output not available from this repository.

Request-a-Copy directly from author or use local Library Get it For Me service.

Request Changes to record.

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > 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:	0951-7715
Official Date:	April 2011
Dates:	Date Event April 2011 Published
Volume:	Volume 24
Number:	Number 4
Page Range:	pp. 1361-1367
DOI:	10.1088/0951-7715/24/4/018
Status:	Peer Reviewed
Publication Status:	Published
Funder:	Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC)
Grant number:	EP/F031807/01 (EPSRC)

Data sourced from Thomson Reuters' Web of Knowledge

Request changes or add full text files to a record

Repository staff actions (login required)

View Item