CENTRAL LIMIT THEOREM FOR TWO-PARAMETER MARTINGALE DIFFERENCES WITH APPLICATION TO STATIONARY RANDOM FIELDS

In this paper, the central limit theorem for two-parameter martingale differences andstationary random fields is obtained. The martingale differences are defined according tothe order of the lattices （s,s）<（t,t） iff s<tor S=tand s<t. An example showsthat this definition may be the weakest condition under which the central limit theorem stillholds. These results are used for the limit distribution of average value and sample autocovar-iances of stationary random fields as well as least squares estimates for some kind of spatialAR models.