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August 2015 Central limit theorems in linear dynamics
Frédéric Bayart
Ann. Inst. H. Poincaré Probab. Statist. 51(3): 1131-1158 (August 2015). DOI: 10.1214/13-AIHP585

Abstract

Given a bounded operator $T$ on a Banach space $X$, we study the existence of a probability measure $\mu$ on $X$ such that, for many functions $f:X\to\mathbb{K}$, the sequence $(f+\cdots+f\circ T^{n-1})/\sqrt{n}$ converges in distribution to a Gaussian random variable.

Étant donné un opérateur $T$ agissant sur un espace de Banach $X$, nous étudions l’existence d’une mesure de probabilité $\mu$ sur $X$ telle que, pour de nombreuses fonctions $f:X\to\mathbb{K}$, la suite $(f+\cdots+f\circ T^{n-1})/\sqrt{n}$ converge en loi vers une variable aléatoire gaussienne.

Citation

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Frédéric Bayart. "Central limit theorems in linear dynamics." Ann. Inst. H. Poincaré Probab. Statist. 51 (3) 1131 - 1158, August 2015. https://doi.org/10.1214/13-AIHP585

Information

Received: 10 May 2013; Revised: 10 September 2013; Accepted: 22 September 2013; Published: August 2015
First available in Project Euclid: 1 July 2015

zbMATH: 1353.47015
MathSciNet: MR3365976
Digital Object Identifier: 10.1214/13-AIHP585

Subjects:
Primary: 47B37

Rights: Copyright © 2015 Institut Henri Poincaré

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Vol.51 • No. 3 • August 2015
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