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Characterization of weak convergence of Birkhoff sums for Gibbs-Markov maps by Gouezel, Sebastien is a scholarly article available to read on EtoBox.

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We investigate limit theorems for Birkhoff sums of locally H\"older functions under the iteration of Gibbs-Markov maps. Aaronson and Denker have given sufficient conditions to have limit theorems in this setting. We show that these conditions are also necessary: there is no exotic limit theorem for Gibbs-Markov maps. Our proofs, valid under very weak regularity assumptions, involve weak perturbation theory and interpolation spaces. For L^2 observables, we also obtain necessary and sufficient conditions to control the speed of convergence in the central limit theorem.

Author

Gouezel, Sebastien

Published

2008

Language

EN