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

By N. Haydn, Matthew Nicol, Andrei Török, Sandro Vaienti. 2014

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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.

Subfields: Economics and Econometrics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/59e131c66e92c8517fd5798d64b209125e4a868f