Stable large deviations for deterministic dynamical systems

TL;DR

This paper establishes large deviation principles for dependent random variables in the domain of attraction of stable laws, including ergodic sums from Gibbs-Markov maps, expanding understanding of probabilistic behavior in dynamical systems.

Contribution

It introduces large deviation results for dependent variables in the domain of attraction of stable laws, covering ergodic sums in dynamical systems driven by Gibbs-Markov maps.

Findings

Large deviations are proven for variables in the domain of attraction of stable laws.

Includes ergodic sums of observables in Gibbs-Markov systems.

Extends large deviation theory to dependent, non-i.i.d. settings.

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.