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).
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).
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@article{CRMATH_2007__345_5_283_0, author = {Klicnarov\'a, Jana and Voln\'y, Dalibor}, title = {An invariance principle for non-adapted processes}, journal = {Comptes Rendus. Math\'ematique}, pages = {283--287}, publisher = {Elsevier}, volume = {345}, number = {5}, year = {2007}, doi = {10.1016/j.crma.2007.05.009}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.05.009/} }
TY - JOUR AU - Klicnarová, Jana AU - Volný, Dalibor TI - An invariance principle for non-adapted processes JO - Comptes Rendus. Mathématique PY - 2007 SP - 283 EP - 287 VL - 345 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.05.009/ DO - 10.1016/j.crma.2007.05.009 LA - en ID - CRMATH_2007__345_5_283_0 ER -
%0 Journal Article %A Klicnarová, Jana %A Volný, Dalibor %T An invariance principle for non-adapted processes %J Comptes Rendus. Mathématique %D 2007 %P 283-287 %V 345 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.05.009/ %R 10.1016/j.crma.2007.05.009 %G en %F CRMATH_2007__345_5_283_0
Klicnarová, Jana; Volný, Dalibor. 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. http://archive.numdam.org/articles/10.1016/j.crma.2007.05.009/
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