Central Limit Theorems and Invariance Principles for Lorenz Attractors
J London Math Soc 76 (2007) 345-364
Mark Holland and Ian Melbourne
Abstract
We prove statistical limit laws for Hölder observations of the Lorenz
attractor, and more generally for geometric Lorenz attractors.
In particular, we prove the almost sure invariance principle
(approximation by Brownian motion). Standard consequences of this
result include the central limit theorem, the law of the iterated logarithm,
and the functional versions of these results.
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