Central limit theorems for sequential and random intermittent dynamical systems

TL;DR

This paper proves central limit theorems for non-stationary and random intermittent dynamical systems, specifically for perturbed Pomeau-Manneville maps, advancing understanding of their statistical behavior.

Contribution

It introduces self-norming and quenched CLTs for sequential and random compositions of perturbed Pomeau-Manneville maps, extending prior results to non-stationary settings.

Findings

Established self-norming CLTs for non-stationary systems.

Proved quenched CLTs for random compositions of these maps.

Enhanced understanding of statistical properties of intermittent dynamical systems.

Abstract

We establish self-norming central limit theorems 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. We also obtain quenched central limit theorems for random compositions of these maps.