Comptes Rendus
Probability Theory
An invariance principle for non-adapted processes
[Principe d'invariance pour processus non-adaptés]
Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 283-287.

Nous présentons un principe d'invariance conditionnel (par rapport à la tribu des ensembles invariants) pour une suite stationnaire non-adaptée de variables aléatoires. Il généralise le principe d'invariance de Wu et Woodroofe (2004, Corollary 3) en utilisant la méthode introduite par Volný (2006). A l'aide d'un exemple, nous montrons que la méthode ne donne pas une généralisation du principe d'invariance de Peligrad et Utev (2005).

We present an invariance principle for a non-adapted stationary sequence of random variables, conditional with respect to the σ-algebra of invariant sets. It is a generalization of an invariance principle of Wu and Woodroofe (2004, Corollary 3) using a method introduced by Volný (2006). An example shows that the method cannot be used directly for a generalization of the invariance principle of Peligrad and Utev (2005).

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Accepté le :
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DOI : 10.1016/j.crma.2007.05.009

Jana Klicnarová 1 ; Dalibor Volný 2

1 Faculty of Economics, University of South Bohemia, Studentská 13, 370 05 České Budějovice, Czech Republic
2 Laboratoire de Mathématiques, Université de Rouen, Technopôle du Madrillet, 76801 Saint-Étienne-du-Rouvray, France
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Jana Klicnarová; Dalibor Volný. An invariance principle for non-adapted processes. Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 283-287. doi : 10.1016/j.crma.2007.05.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.05.009/

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