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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
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Official URL: http://dx.doi.org/10.1214/08-AOP410
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 > Mathematics | ||||
| Journal or Publication Title: | The Annals of Probability | ||||
| Publisher: | Institute of Mathematical Statistics | ||||
| ISSN: | 0091-1798 | ||||
| Official Date: | 2009 | ||||
| Dates: |
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| 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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