, Volume 110, Issue 3, pp 397-426

A central limit theorem for stationary random fields

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.