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.
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In particular, the position variable of the planar periodic Lorentz gas with finite horizon approximates a two-dimensional Brownian motion.
Publié le : 2009-03-15
Classification:
Almost sure invariance principle,
nonuniform hyperbolicity,
Lorentz gases,
Brownian motion,
Young towers,
37A50,
37D20,
37D25,
37D50,
60F17
@article{1241099919,
author = {Melbourne, Ian and Nicol, Matthew},
title = {A vector-valued almost sure invariance principle for hyperbolic dynamical systems},
journal = {Ann. Probab.},
volume = {37},
number = {1},
year = {2009},
pages = { 478-505},
language = {en},
url = {http://dml.mathdoc.fr/item/1241099919}
}
Melbourne, Ian; Nicol, Matthew. A vector-valued almost sure invariance principle for hyperbolic dynamical systems. Ann. Probab., Tome 37 (2009) no. 1, pp. 478-505. http://gdmltest.u-ga.fr/item/1241099919/