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arXiv · 1811.11170

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

Olli Hella·Juho Leppänen
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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.

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Olli Hella, Juho Leppänen. 2018-11-27. Central limit theorems with a rate of convergence for time-dependent intermittent maps. https://doi.org/10.1142/s0219493720500252

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