On the Weak Invariance Principle for Stationary Sequences under Projective Criteria

Florence Merlevède () and Magda Peligrad ()
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Florence Merlevède: Université Paris VI, et C.N.R.S UMR 7599
Magda Peligrad: University of Cincinnati

Journal of Theoretical Probability, 2006, vol. 19, issue 3, 647-689

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.

Keywords: Central limit theorem; weak invariance principle; projective criteria; strong mixing sequences; martingale approximation; 60 F 05; 60 F 17 (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10959-006-0029-y

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