# Comparison between criteria leading to the weak invariance principle

Abstract : The aim of this paper is to compare various criteria leading to the central limit theorem and the weak invariance principle. These criteria are the martingale-coboundary decomposition developed by Gordin in Dokl. Akad. Nauk SSSR 188 (1969), the projective criterion introduced by Dedecker in Probab. Theory Related Fields 110 (1998), which was subsequently improved by Dedecker and Rio in Ann. Inst. H. Poincar\'{e} Probab. Statist. 36 (2000) and the condition introduced by Maxwell and Woodroofe in Ann. Probab. 28 (2000) later improved upon by Peligrad and Utev in Ann. Probab. 33 (2005). We prove that in every ergodic dynamical system with positive entropy, if we consider two of these criteria, we can find a function in $\mathbb{L}^2$ satisfying the first but not the second.
Type de document :
Article dans une revue
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2008, 44 (2), pp.324-340. 〈10.1214/07-AIHP123〉
Domaine :

https://hal.archives-ouvertes.fr/hal-00291468
Contributeur : Olivier Durieu <>
Soumis le : vendredi 27 juin 2008 - 11:25:55
Dernière modification le : mercredi 15 novembre 2017 - 16:00:01

### Citation

Olivier Durieu, Dalibor Volný. Comparison between criteria leading to the weak invariance principle. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2008, 44 (2), pp.324-340. 〈10.1214/07-AIHP123〉. 〈hal-00291468〉

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