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### A note on diffusion limits of chaotic skew-product flows

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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 0951-7715

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1088/0951-7715/24/4/018

## 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 |
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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: | 0951-7715 |

Official Date: | April 2011 |

Volume: | Volume 24 |

Number: | Number 4 |

Page Range: | pp. 1361-1367 |

Identification Number: | 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) |

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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