On the Asymptotic moments and Edgeworth expansions for some processes in\n random dynamical environment

2018/12/17 by Yeor Hafouta, Hafouta, Yeor · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1812.06924

openalex publication_date 2018/12/17 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28

Abstract

We prove that certain asymptotic moments exist for some random distance\nexpanding dynamical systems and Markov chains in random dynamical environment,\nand compute them in terms of the derivatives at the 0 of an appropriate\npressure function. It will follow that these moments satisfy the relations that\nthe asymptotic moments gam_k=\lim_n\→\∞n^{-[ frac\nk2]} bbE(\∑_i=1ⁿ X_i)^k of sums of independent and identically\ndistributed random variables satisfy. We will also obtain certain (Edgeworth)\nasymptotic expansions related to the central limit theorem for such processes.\nOur proofs rely on a (parametric) random complex Ruelle-Perron-Frobenius\ntheorem, which replaces some the spectral techniques which are used in\nliterature in order to obtain limit theorems for deterministic dynamical\nsystems and Markov chains.\n

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