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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 ISSN 0022-1236.
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Official URL: https://doi.org/10.1016/j.jfa.2017.01.015
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: |
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| 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 | ||||||||
| Date of first compliant deposit: | 2 February 2017 | ||||||||
| Date of first compliant Open Access: | 23 February 2018 | ||||||||
| 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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