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Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas
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Demers, Mark, Melbourne, Ian and Nicol, Matthew (2020) Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas. Nonlinearity, 33 (8). 4095. doi:10.1088/1361-6544/ab7d22 ISSN 0951-7715.
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WRAP-Martingale-approximations-anisotropic-Banach-spaces-application-time-one-map-Lorentz-gas-Melbourne-2020.pdf - Accepted Version - Requires a PDF viewer. Download (905Kb) | Preview |
Official URL: https://doi.org/10.1088/1361-6544/ab7d22
Abstract
In this paper, we show how the Gordin martingale approximation method fits into the anisotropic Banach space framework. In particular, for the time-one map of a finite horizon planar periodic Lorentz gas, we prove that Hölder observables satisfy statistical limit laws such as the central limit theorem and associated invariance principles. Previously, these properties were known only for a restricted class of observables, excluding for instance velocity.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Martingales (Mathematics), Method of steepest descent (Numerical analysis), Banach spaces | ||||||||||||
Journal or Publication Title: | Nonlinearity | ||||||||||||
Publisher: | Institute of Physics Publishing Ltd. | ||||||||||||
ISSN: | 0951-7715 | ||||||||||||
Official Date: | 2 July 2020 | ||||||||||||
Dates: |
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Volume: | 33 | ||||||||||||
Number: | 8 | ||||||||||||
Article Number: | 4095 | ||||||||||||
DOI: | 10.1088/1361-6544/ab7d22 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Reuse Statement (publisher, data, author rights): | This is an author-created, un-copyedited version of an article accepted for publication in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6544/ab7d22 | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Copyright Holders: | © 2020 IOP Publishing Ltd & London Mathematical Society | ||||||||||||
Date of first compliant deposit: | 12 March 2020 | ||||||||||||
Date of first compliant Open Access: | 2 July 2021 | ||||||||||||
RIOXX Funder/Project Grant: |
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