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A central limit theorem for stationary random fields
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  • Published: March 1998

A central limit theorem for stationary random fields

  • Jérôme Dedecker1 

Probability Theory and Related Fields volume 110, pages 397–426 (1998)Cite this article

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Summary.

We prove a central limit theorem for strictly stationary random fields under a projective assumption. Our criterion is similar to projective criteria for stationary sequences derived from Gordin's theorem about approximating martingales. However our approach is completely different, for we establish our result by adapting Lindeberg's method. The criterion that it provides is weaker than martingale-type conditions, and moreover we obtain as a straightforward consequence, central limit theorems for α-mixing or φ-mixing random fields.

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Authors and Affiliations

  1. URA n° 0743 CNRS, Université de Paris-Sud, Bât. 425, Mathématique, F-91405 Orsay Cedex, France e-mail:Jerome.Dedecker@matups.matups.fr, , , , , , FR

    Jérôme Dedecker

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  1. Jérôme Dedecker
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Received: 19 February 1997 / In revised form: 2 September 1997

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Dedecker, J. A central limit theorem for stationary random fields. Probab Theory Relat Fields 110, 397–426 (1998). https://doi.org/10.1007/s004400050153

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  • Issue Date: March 1998

  • DOI: https://doi.org/10.1007/s004400050153

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  • Mathematics Subject Classification (1991): 60 F 05
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