Almost sure invariance principle for random dynamical systems via Gouëzel's approach. (20th August 2021)

• Record Type: Journal Article
• Authors: Dragičević, D.; Hafouta, Y
• Is Part Of: Nonlinearity. Volume 34:Number 10(2021)
• Page Start: 6773
• Page End: 6798
• Publication Date: 2021-08-20
• Subjects: almost sure invariance principle -- random dynamical systems -- hyperbolic dynamical systems; 37H99 -- 37C30 -- 60F17; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac14a1
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We extend the spectral approach of S Gouëzel for the vector-valued almost sure invariance principle (ASIP) to certain classes of non-stationary sequences with a weaker control over the behaviour of the covariance matrices, assuming only linear growth. Then we apply this extension to obtain a quenched vector-valued ASIP for random perturbations of a fixed Anosov diffeomorphism as well as random perturbations of a billiard map associated to the periodic Lorentz gas. We also consider certain classes of random piecewise expanding maps.