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arXiv · 1811.09094

Rates in almost sure invariance principle for quickly mixing dynamical systems

C Cuny·J Dedecker·A Korepanov·Florence Merlevède
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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 $\ge$ 2. Specifically, we consider nonuniformly expanding maps with exponential and stretched exponential decay of correlations, with one-dimensional H{\"o}lder continuous observables.

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C Cuny, J Dedecker, A Korepanov, Florence Merlevède. 2018-11-22. Rates in almost sure invariance principle for quickly mixing dynamical systems. https://arxiv.org/abs/1811.09094

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