Almost sure invariance principle for sequential and non-stationary dynamical systems

2014/06/17 by Haydn, N., Nicol, M., Tôrôk, A. +1 · 4 citations
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1406.4266

Abstract

We establish almost sure invariance principles, a strong form of approximation by Brownian motion, for non-stationary time-series arising as observations on dynamical systems. Our examples include observations on sequential expanding maps, perturbed dynamical systems, non-stationary sequences of functions on hyperbolic systems as well as applications to the shrinking target problem in expanding systems.

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• Decay of correlations and limit theorems for random intermittent maps
• Statistical properties of Markov shifts: part II-LLT
• Statistical properties of Markov shifts (part I)

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