Independence of Four Projective Criteria for the Weak Invariance Principle

Abstract : Let $(X_i)_{i\in\Z}$ be a regular stationary process for a given filtration. The weak invariance principle holds under the condition $\sum_{i\in\Z}\|P_0(X_i)\|_2<\infty$ (see Hannan (1979)}, Dedecker and Merlevède (2003), Deddecker, Merlevéde and Volný (2007)). In this paper, we show that this criterion is independent of other known criteria: the martingale-coboundary decomposition of Gordin (see Gordin (1969, 1973)), the criterion of Dedecker and Rio (see Dedecker and Rio (2000)) and the condition of Maxwell and Woodroofe (see Maxwell and Woodroofe (2000), Peligrade and Utev (2005), Volný (2006, 2007)).
Type de document :
Article dans une revue
ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2009, 5, pp.21-27
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00291499
Contributeur : Olivier Durieu <>
Soumis le : vendredi 27 juin 2008 - 11:27:03
Dernière modification le : mercredi 15 novembre 2017 - 16:00:01

Identifiants

  • HAL Id : hal-00291499, version 1
  • ARXIV : 0804.1848

Collections

Citation

Olivier Durieu. Independence of Four Projective Criteria for the Weak Invariance Principle. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2009, 5, pp.21-27. 〈hal-00291499〉

Partager

Métriques

Consultations de la notice

73