Electron.J. Probab. 19 (2014) 1-30.
Sébastien Gouëzel and Ian Melbourne
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.