Probability theory
A central limit theorem for fields of martingale differences
Comptes Rendus. Mathématique, Volume 353 (2015) no. 12, pp. 1159-1163.

We prove a central limit theorem for stationary random fields of martingale differences fTi_, 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.

Le théorème limite centrale pour un champ aléatoire fTi_, 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.

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Published online:
DOI: 10.1016/j.crma.2015.09.017
Volný, Dalibor 1

1 Laboratoire de mathématiques Raphaël-Salem, UMR 6085, Université de Rouen, France
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Volný, Dalibor. 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. http://www.numdam.org/articles/10.1016/j.crma.2015.09.017/

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