Gouëzel, Sébastien Berry–Esseen theorem and local limit theorem for non uniformly expanding maps. (English) Zbl 1134.60323 Ann. Inst. Henri Poincaré, Probab. Stat. 41, No. 6, 997-1024 (2005). Summary: In Young towers with sufficiently small tails, the Birkhoff sums of Hölder continuous functions satisfy a central limit theorem with speed \(O(1/\sqrt n)\), and a local limit theorem. This implies the same results for many non uniformly expanding dynamical systems, namely those for which a tower with sufficiently fast returns can be constructed. Cited in 51 Documents MSC: 60F15 Strong limit theorems 37A30 Ergodic theorems, spectral theory, Markov operators 37A50 Dynamical systems and their relations with probability theory and stochastic processes 37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 60F05 Central limit and other weak theorems PDFBibTeX XMLCite \textit{S. Gouëzel}, Ann. Inst. Henri Poincaré, Probab. Stat. 41, No. 6, 997--1024 (2005; Zbl 1134.60323) Full Text: DOI arXiv Numdam EuDML