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arXiv · 2208.00518

Explicit conditions for the CLT and related results for non-uniformly partially expanding random dynamical systems via effective RPF rates

Yeor Hafouta
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Abstract

The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as stochastic processes together with some random Gibbs measure. More precisely, we prove a central limit theorem (CLT), an almost sure invariance principle, a moderate deviations principle, Berry-Esseen type estimates and a moderate local central limit theorem for random Birkhoff sums generated by a non-uniformly partially expanding dynamical systems $T_\omega$ and a random Gibbs measure $\mu_\omega$ corresponding to a random potential $\phi_\omega$ with a sufficiently regular variation.

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Yeor Hafouta. 2022-07-31. Explicit conditions for the CLT and related results for non-uniformly partially expanding random dynamical systems via effective RPF rates. https://arxiv.org/abs/2208.00518

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