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

Dedecker, Jérôme1
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, Tome 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.

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Accepté le :
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DOI : 10.1016/j.crma.2015.03.010
Dedecker, Jérôme 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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Dedecker, Jérôme. On the optimality of McLeish's conditions for the central limit theorem. Comptes Rendus. Mathématique, Tome 353 (2015) no. 6, pp. 557-561. doi : 10.1016/j.crma.2015.03.010. http://www.numdam.org/articles/10.1016/j.crma.2015.03.010/

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