Rates in almost sure invariance principle for quickly mixing dynamical systems

Abstract : For a large class of quickly mixing dynamical systems, we prove that the error in the almost sure approximation with a Brownian motion is of order O((log n)^a) with a ≥ 2. Specifically, we consider nonuniformly expanding maps with exponential and stretched exponential decay of correlations, with one-dimensional Hölder continuous observables.
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https://hal.archives-ouvertes.fr/hal-01929238
Contributor : Jérôme Dedecker <>
Submitted on : Wednesday, November 21, 2018 - 9:50:56 AM
Last modification on : Thursday, April 11, 2019 - 4:02:50 PM
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  • HAL Id : hal-01929238, version 1
  • ARXIV : 1811.09094

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C Cuny, J Dedecker, A Korepanov, Florence Merlevède. Rates in almost sure invariance principle for quickly mixing dynamical systems. 2018. ⟨hal-01929238⟩

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