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


Authors: Nicolai Haydn, Matthew Nicol, Andrew Török and Sandro Vaienti
Journal: Trans. Amer. Math. Soc. 369 (2017), 5293-5316
MSC (2010): Primary 37C99
DOI: https://doi.org/10.1090/tran/6812
Published electronically: January 9, 2017
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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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Additional Information

Nicolai Haydn
Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
Email: nhaysdn@math.usc.edu

Matthew Nicol
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: nicol@math.uh.edu

Andrew Török
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204 – and – Institute of Mathematics of the Romanian Academy, P.O. Box 1–764, RO-70700 Bucharest, Romania
Email: torok@math.uh.edu

Sandro Vaienti
Affiliation: Aix Marseille Université, Université de Toulon, CNRS, CPT, Marseille, France
Email: vaienti@cpt.univ-mrs.fr

DOI: https://doi.org/10.1090/tran/6812
Received by editor(s): June 17, 2014
Received by editor(s) in revised form: August 18, 2015, and August 20, 2015
Published electronically: January 9, 2017
Article copyright: © Copyright 2017 American Mathematical Society