Naslov
Limit theorems for random expanding or Anosov dynamical systems and vector-valued observables

Autori
Dragičević, Davor ; Hafouta, Yeor

Izvornik
Annales henri poincare (1424-0637) 21 (2020), 12; 3869-3917

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
limit theorems ; hyperbolic random dynamical systems ; piecewise expanding random dynamical systems

Sažetak
The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic (Anosov) dynamics developed by the first author \textit{; ; ; ; et al}; ; ; ; . to establish quenched versions of the large deviation principle, central limit theorem and the local central limit theorem for \emph{; ; ; ; vector-valued}; ; ; ; observables. We stress that the previous works considered exclusively the case of scalar- valued observables. In another direction, we show that this method can be used to establish a variety of new limit laws (either for scalar or vector- valued observables) that have not been discussed previously in the literature for the classes of dynamics we consider. More precisely, we establish the moderate deviations principle, concentration inequalities, Berry- Esseen estimates as well as Edgeworth and large deviation expansions. Although our techniques rely on the approach developed in the previous works of the first author \textit{; ; ; ; et al}; ; ; ; ., we emphasize that our arguments require several nontrivial adjustments as well as new ideas.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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