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Deterministic homogenization for fast-slow systems with chaotic noise

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Kelly, David and Melbourne, Ian (2017) Deterministic homogenization for fast-slow systems with chaotic noise. Journal of Functional Analysis, 272 (10). pp. 4063-4102. doi:10.1016/j.jfa.2017.01.015

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Official URL: https://doi.org/10.1016/j.jfa.2017.01.015

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Abstract

Consider a fast-slow system of ordinary differential equations of the form x˙=a(x,y)+ε−1b(x,y), y˙=ε−2g(y), where it is assumed that b averages to zero under the fast flow generated by g. We give conditions under which solutions x to the slow equations converge weakly to an It\^o diffusion X as ε→0. The drift and diffusion coefficients of the limiting stochastic differential equation satisfied by X are given explicitly.

Our theory applies when the fast flow is Anosov or Axiom A, as well as to a large class of nonuniformly hyperbolic fast flows (including the one defined by the well-known Lorenz equations), and our main results do not require any mixing assumptions on the fast flow.

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, Anosov flows
Journal or Publication Title: Journal of Functional Analysis
Publisher: Academic Press
ISSN: 0022-1236
Official Date: 15 May 2017
Dates:
DateEvent
15 May 2017Published
23 February 2017Available
31 January 2017Accepted
Volume: 272
Number: 10
Page Range: pp. 4063-4102
DOI: 10.1016/j.jfa.2017.01.015
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Great Britain. Office for Nuclear Regulation (ONR), European Research Council (ERC)
Grant number: N00014-12-1-0257 (ONR), European Advanced Grant StochExtHomog ERC AdG 320977 (ERC)

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