Central limit theorems with a rate of convergence for time-dependent intermittent maps

Abstract

We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate of convergence. For maps chosen from a certain parameter range, but without additional assumptions on how the maps vary with time, we obtain a self-normalized CLT provided that the variances of the partial sums grow sufficiently fast. When the maps are chosen randomly according to a shift-invariant probability measure, we identify conditions under which the quenched CLT holds, assuming fiberwise centering. Finally, we show a multivariate CLT for intermittent quasistatic systems. Our approach is based on Stein's method of normal approximation.

arXiv comment24 pages. Final peer-reviewed manuscript. To appear in Stochastics and Dynamics (https://doi.org/10.1142/S0219493720500252)

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• Sunklodas' approach to normal approximation for time-dependent dynamical systems