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Article Dans Une Revue Stochastics and Dynamics Année : 2020

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

Résumé

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-norming 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 quasi-static systems. Our approach is based on Stein’s method of normal approximation.

Dates et versions

hal-03944135 , version 1 (17-01-2023)

Identifiants

Citer

Olli Hella, Juho Leppänen. Central limit theorems with a rate of convergence for time-dependent intermittent maps. Stochastics and Dynamics, 2020, 20 (04), pp.2050025. ⟨10.1142/S0219493720500252⟩. ⟨hal-03944135⟩
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