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On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria

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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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Authors and Affiliations

  1. Laboratoire de Statistique Théorique et Appliquée, Université Paris VI, Boîte 158, Plateau A, 8 ème étage, 175 rue du Chevaleret, 75013, Paris, France

    Jérôme Dedecker

  2. Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI, et C.N.R.S UMR 7599, Boîte 188, 175 rue du Chevaleret, 75013, Paris, France

    Florence Merlevède

  3. LMRS, Université de Rouen, Avenue de l’Université, 76801, Saint Etienne du Rouvray, France

    Dalibor Volný

Authors
  1. Jérôme Dedecker
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  2. Florence Merlevède
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  3. Dalibor Volný
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Correspondence to Jérôme Dedecker.

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Dedecker, J., Merlevède, F. & Volný, D. On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria. J Theor Probab 20, 971–1004 (2007). https://doi.org/10.1007/s10959-007-0090-1

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  • DOI: https://doi.org/10.1007/s10959-007-0090-1

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