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arXiv · 1702.07691

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

Jason Atnip
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Abstract

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 a fiberwise spectral gap property as well as an exponential decay of correlations in the base, then, developing on Gou\"{e}zel's approach, the system satisfies the almost sure invariance principle. The result is then applied to uniformly expanding random systems like those studied by Denker and Gordin and Mayer, Skorulski, and Urba\'nski.

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Jason Atnip. 2017-02-24. An Almost Sure Invariance Principle for Several Classes of Random Dynamical Systems. https://arxiv.org/abs/1702.07691

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