On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria |
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| Authors: | Jérôme Dedecker Florence Merlevède Dalibor Volný |
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| Institution: | 1.Laboratoire de Statistique Théorique et Appliquée,Université Paris VI,Paris,France;2.Laboratoire de Probabilités et Modèles Aléatoires,Université Paris VI, et C.N.R.S UMR 7599,Paris,France;3.LMRS,Université de Rouen,Saint Etienne du Rouvray,France |
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| Abstract: | In this paper we study the central limit theorem and its weak invariance principle for sums of non-adapted stationary sequences,
under different normalizations. Our conditions involve the conditional expectation of the variables with respect to a given
σ-algebra, as done in Gordin (Dokl. Akad. Nauk SSSR 188, 739–741, 1969) and Heyde (Z. Wahrsch. verw. Gebiete 30, 315–320, 1974). These conditions are well adapted to a large variety of examples, including linear processes with dependent innovations
or regular functions of linear processes. |
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| Keywords: | Central limit theorem Weak invariance principle Projective criteria Martingale approximation Functions of linear processes |
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