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

Haydn, Nicolai; Nicol, Matthew; Török, Andrew; Vaienti, Sandro

doi:10.1090/tran/6812

Almost sure invariance principle for sequential and non-stationary dynamical systems
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by Nicolai Haydn, Matthew Nicol, Andrew Török and Sandro Vaienti PDF

Trans. Amer. Math. Soc. 369 (2017), 5293-5316 Request permission

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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