Orthomartingale-coboundary decomposition for stationary random fields

Abstract

We provide a new projective condition for a stationary real random field indexed by the lattice [Formula: see text] to be well approximated by an orthomartingale in the sense of Cairoli (1969). Our main result can be viewed as a multidimensional version of the martingale-coboundary decomposition method which the idea goes back to Gordin (1969). It is a powerful tool for proving limit theorems or large deviations inequalities for stationary random fields when the corresponding result is valid for orthomartingales.