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

Jérôme Dedecker (), Florence Merlevède () and Dalibor Volný ()
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Jérôme Dedecker: Université Paris VI
Florence Merlevède: Université Paris VI, et C.N.R.S UMR 7599
Dalibor Volný: Université de Rouen

Journal of Theoretical Probability, 2007, vol. 20, issue 4, 971-1004

Abstract: 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.

Keywords: Central limit theorem; Weak invariance principle; Projective criteria; Martingale approximation; Functions of linear processes (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10959-007-0090-1

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