In this paper we provide necessary and sufficient conditions for the mean square approximation of a random field with an ortho-martingale. The conditions are formulated in terms of projective criteria. Applications are given to linear and nonlinear random fields with independent innovations.
Two sufficient conditions for Poisson approximations in the ferromagnetic Ising model
Quenched invariance principles for orthomartingale-like sequences
On the normal approximation for random fields via martingale methods
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