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

2022/07/31 by Yeor Hafouta, Hafouta, Yeor · 6 citations
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2208.00518

openalex publication_date 2022/07/31 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

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_ω and a random Gibbs measure μ_ω corresponding to a random potential ϕ_ω with a sufficiently regular variation.

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