Moment bounds and concentration inequalities for slowly mixing dynamical systems

Sébastien Gouëzel (Université Rennes 1)
Ian Melbourne (University of Warwick)

Abstract


We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit theorem with nonstandard scaling $(n\log n)^{1/2}$.

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Pages: 1-30

Publication Date: October 3, 2014

DOI: 10.1214/EJP.v19-3427

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