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A vector-valued almost sure invariance principle for hyperbolic dynamical systems

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Melbourne, Ian and Nicol, Matthew (2009) A vector-valued almost sure invariance principle for hyperbolic dynamical systems. The Annals of Probability, Vol.37 (No.2). pp. 478-505. doi:10.1214/08-AOP410 ISSN 0091-1798.

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Official URL: http://dx.doi.org/10.1214/08-AOP410

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Abstract

We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Hölder observables of large classes of nonuniformly hyperbolic dynamical systems. These systems include Axiom A diffeomorphisms and flows as well as systems modeled by Young towers with moderate tail decay rates.

In particular, the position variable of the planar periodic Lorentz gas with finite horizon approximates a two-dimensional Brownian motion.

Item Type: Journal Article
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title: The Annals of Probability
Publisher: Institute of Mathematical Statistics
ISSN: 0091-1798
Official Date: 2009
Dates:
DateEvent
2009Published
Volume: Vol.37
Number: No.2
Page Range: pp. 478-505
DOI: 10.1214/08-AOP410
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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