Strong regularity for stationary discrete random fields is discussed. An extension of the classical Beurling's Theorem to functions of several variables is given. Necessary and sufficient conditions for the moving average representation of stationary random fields are obtained. A recipe formula for the best linear extrapolator is also given.
"Extrapolation and Moving Average Representation for Stationary Random Fields and Beurling's Theorem." Ann. Probab. 12 (1) 120 - 132, February, 1984. https://doi.org/10.1214/aop/1176993377