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Berry–Esseen theorem and local limit theorem for non uniformly expanding maps. (English) Zbl 1134.60323

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.

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
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