Stable large deviations for deterministic dynamical systems

Abstract

We obtain large deviations for a class of dependent random variables in the domain of attraction of an $\alpha$-stable law, $\alpha \in (0,1)\cup (1,2]$. This class includes ergodic sums of observables in the domain of attraction of an $\alpha$-stable law driven by Gibbs-Markov maps.

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