# An Indicator Function Limit Theorem in Dynamical Systems

Abstract : We show by a constructive proof that in all aperiodic dynamical system, for all sequences $(a_n)_{n\in\N}\subset\R_+$ such that $a_n\nearrow\infty$ and $\frac{a_n}{n}\to 0$ as $n\to\infty$, there exists a set $A\in\A$ having the property that the sequence of the distributions of $(\frac{1}{a_{n}}S_{n}(\ind_A-\mu(A)))_{n\in\N}$ is dense in the space of all probability measures on $\R$.
Type de document :
Article dans une revue
Stochastics and Dynamics, World Scientific Publishing, 2011, 11 (4), pp.681--690. 〈10.1142/S0219493711003504〉
Domaine :
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https://hal.archives-ouvertes.fr/hal-00331666
Contributeur : Olivier Durieu <>
Soumis le : vendredi 17 octobre 2008 - 11:42:11
Dernière modification le : jeudi 7 février 2019 - 17:46:39

### Citation

Olivier Durieu, Dalibor Volny. An Indicator Function Limit Theorem in Dynamical Systems. Stochastics and Dynamics, World Scientific Publishing, 2011, 11 (4), pp.681--690. 〈10.1142/S0219493711003504〉. 〈hal-00331666〉

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