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Comptes Rendus Mathématique
Volume 353, n° 12
pages 1159-1163 (décembre 2015)
Doi : 10.1016/j.crma.2015.09.017
Received : 22 Mars 2015 ;  accepted : 17 September 2015
A central limit theorem for fields of martingale differences
Théorème limite centrale pour des champs de différences de martingale
 

Dalibor Volný
 Laboratoire de mathématiques Raphaël-Salem, UMR 6085, Université de Rouen, France 

Abstract

We prove a central limit theorem for stationary random fields of martingale differences  ,  , where   is a   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   action is supposed.

The full text of this article is available in PDF format.
Résumé

Le théorème limite centrale pour un champ aléatoire  ,  , 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   est supposée.

The full text of this article is available in PDF format.


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