Almost Surely Invariance Principle for Non-stationary and Random Intermittent Dynamical Systems

2019/03/23 by Yaofeng Su, Su, Yaofeng · 1 citation
Economics, Econometrics and Finance · Mathematics · #37A25 #37E05 #60F17 #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1903.09758

openalex publication_date 2019/03/23 · openalex created_date 2019/04/01 · openalex updated_date 2026/07/28

Abstract

We establish almost sure invariance principles (ASIP), a strong form of approximation by Brownian motion, for non-stationary time series arising as observations on sequential maps possessing an indifferent fixed point. These transformations are obtained by perturbing the slope in the Pomeau-Manneville map. Quenched ASIP for random compositions of these maps is also obtained.

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• Decay of correlations and limit theorems for random intermittent maps

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