Rate of Convergence in the Weak Invariance Principle for Deterministic Systems

  • Marios Antoniou
  • Ian MelbourneEmail author


We obtain the first results on convergence rates in the Prokhorov metric for the weak invariance principle (functional central limit theorem) for deterministic dynamical systems. Our results hold for uniformly expanding/hyperbolic (Axiom A) systems, as well as nonuniformly expanding/hyperbolic systems such as dispersing billiards, Hénon-like attractors, Viana maps and intermittent maps. As an application, we obtain convergence rates for deterministic homogenization in multiscale systems.


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This research was supported in part by a European Advanced Grant StochExtHomog (ERC AdG 320977).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK

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