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On the Weak Invariance Principle for Stationary Sequences under Projective Criteria |
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| Authors: | Florence Merlevède Magda Peligrad |
| Affiliation: | 1. Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI, et C.N.R.S UMR 7599, Bo?te 188, 175 rue du Chevaleret, 75 013, Paris, France 2. Department of Mathematical Sciences, University of Cincinnati, PO Box 210025, Cincinnati, OH, 45221-0025, USA |
| Abstract: | In this paper, we study the central limit theorem and its weak invariance principle for sums of a stationary sequence of random variables, via a martingale decomposition. Our conditions involve the conditional expectation of sums of random variables with respect to the distant past. The results contribute to the clarification of the central limit question for stationary sequences. Magda Peligrad is supported in part by a Charles Phelps Taft research support grant at the Univeristy of Cincinnati and the NSA grant H98230-05-1-0066. |
| Keywords: | Central limit theorem weak invariance principle projective criteria strong mixing sequences martingale approximation |
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