Comptes Rendus
no. 6
Probability theory
On the optimality of McLeish's conditions for the central limit theorem
[Sur l'optimalité des conditions de McLeish pour le théorème limite central]

Présenté par : the Editorial Board

Jérôme Dedecker1
1 Laboratoire MAP5, CNRS UMR 8145, Université Paris-Descartes, Sorbonne Paris Cité, 45, rue des Saints-Pères, 75270 Paris cedex 06, France
Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 557-561.

Nous construisons une famille de suites strictement stationnaires et ergodiques pour lesquelles le théorème limite central n'a pas lieu. Ces exemples montrent que les conditions de McLeish pour le théorème limite central sont optimales en un sens précis.

We construct a family of stationary ergodic sequences for which the central limit theorem (CLT) does not hold. These examples show that McLeish's conditions for the CLT are sharp in a precise sense.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.03.010

Jérôme Dedecker 1

1 Laboratoire MAP5, CNRS UMR 8145, Université Paris-Descartes, Sorbonne Paris Cité, 45, rue des Saints-Pères, 75270 Paris cedex 06, France 
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Jérôme Dedecker. On the optimality of McLeish's conditions for the central limit theorem. Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 557-561. doi : 10.1016/j.crma.2015.03.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.03.010/

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