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

Autor:	Hella, Olli, Leppänen, Juho
Rok vydání:	2018
Předmět:	Mathematics - Dynamical Systems Mathematics - Probability 37C60 37D25 60F05
Druh dokumentu:	Working Paper
DOI:	10.1142/S0219493720500252
Popis:	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. Comment: 24 pages. Final peer-reviewed manuscript. To appear in Stochastics and Dynamics (https://doi.org/10.1142/S0219493720500252)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1811.11170 Zobrazit plný text záznamu View this record from Arxiv