Comptes Rendus
no. 12
Probability theory
A central limit theorem for fields of martingale differences
[Théorème limite centrale pour des champs de différences de martingale]

Présenté par : Jean-François Le Gall

Dalibor Volný1
1 Laboratoire de mathématiques Raphaël-Salem, UMR 6085, Université de Rouen, France
Comptes Rendus. Mathématique, Volume 353 (2015) no. 12, pp. 1159-1163.

Le théorème limite centrale pour un champ aléatoire f∘Ti_, i_∈Zd, de différences d'une martingale est démontré. Le résultat est connu pour les champs aléatoires de Bernoulli ; ici, l'ergodicité d'un seul générateur de l'action Ti_ est supposée.

We prove a central limit theorem for stationary random fields of martingale differences f∘Ti_, i_∈Zd, where Ti_ is a Zd action and the martingale is given by a commuting filtration. The result has been known for Bernoulli random fields; here only ergodicity of one of commuting transformations generating the Zd action is supposed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.09.017
Dalibor Volný 1

1 Laboratoire de mathématiques Raphaël-Salem, UMR 6085, Université de Rouen, France 
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Dalibor Volný. A central limit theorem for fields of martingale differences. Comptes Rendus. Mathématique, Volume 353 (2015) no. 12, pp. 1159-1163. doi : 10.1016/j.crma.2015.09.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.09.017/

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