Probability Theory and Related Fields

, Volume 110, Issue 3, pp 397–426

A central limit theorem for stationary random fields

  • Jérôme Dedecker

DOI: 10.1007/s004400050153

Cite this article as:
Dedecker, J. Probab Theory Relat Fields (1998) 110: 397. doi:10.1007/s004400050153


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.

Mathematics Subject Classification (1991): 60 F 05 

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

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

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