In this paper we provide necessary and sufficient conditions for the mean square approximation of a random field by an ortho-martingale. The conditions are formulated in terms of projective criteria. Applications are given to linear and nonlinear random fields with independent innovations.
"Martingale approximations for random fields." Electron. Commun. Probab. 23 1 - 9, 2018. https://doi.org/10.1214/18-ECP128