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March 2009 A vector-valued almost sure invariance principle for hyperbolic dynamical systems
Ian Melbourne, Matthew Nicol
Ann. Probab. 37(2): 478-505 (March 2009). DOI: 10.1214/08-AOP410


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.


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Ian Melbourne. Matthew Nicol. "A vector-valued almost sure invariance principle for hyperbolic dynamical systems." Ann. Probab. 37 (2) 478 - 505, March 2009.


Published: March 2009
First available in Project Euclid: 30 April 2009

zbMATH: 1176.37006
MathSciNet: MR2510014
Digital Object Identifier: 10.1214/08-AOP410

Primary: 37A50 , 37D20 , 37D25 , 37D50 , 60F17

Keywords: almost sure invariance principle , Brownian motion , Lorentz gases , nonuniform hyperbolicity , Young towers

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 2 • March 2009
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