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arXiv:1702.07691 [math.DS]AbstractReferencesReviewsResources

An Almost Sure Invariance Principle for Several Classes of Random Dynamical Systems

Jason Atnip

Published 2017-02-24Version 1

In this paper we deal with a large class of dynamical systems having a version of the spectral gap property. Our primary class of systems comes from random dynamics, but we also deal with the deterministic case. We show that if a random dynamical system has the spectral gap property, then, developing on Gou\"{e}zel's approach, then the system satisfies the almost sure invariance principle. The result is then applied to random systems of transcendental functions, uniformly expanding random systems, and random shifts of finite type with weakly positive transfer operators.

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