Variations around Eagleson's Theorem on mixing limit theorems for dynamical systems
Résumé
Eagleson's Theorem asserts that, given a probability-preserving map, if
renormalized Birkhoff sums of a function converge in distribution, then
they also converge with respect to any probability measure which is
absolutely continuous with respect to the invariant one. We prove a version
of this result for almost sure limit theorems, extending results of
Korepanov. We also prove a version of this result, in mixing systems, when
one imposes a conditioning both at time 0 and at time n.
Domaines
Systèmes dynamiques [math.DS]
Origine : Fichiers produits par l'(les) auteur(s)
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