Rates in almost sure invariance principle for quickly mixing dynamical systems

2018/11/22 by Cuny, C, Dedecker, J, Korepanov, A +1 · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1811.09094

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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