Orthomartingale-coboundary decomposition for stationary random fields

Mohamed El Machkouri (1) , Davide Giraudo (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We provide a new projective condition for a stationary real random field indexed by the lattice $\mathbb Z^d$ to be well approximated by an orthomartingale in the sense of Cairoli (1969). Ourmain 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 powerfull tool for proving limit theorems or large deviations inequalities for stationary random fields when the corresponding result is valid for orthomartingales.

Mots clés: orthomartingales; invariance principle; random fields

Domaines: Probabilités [math.PR]

Mohamed El Machkouri, Davide Giraudo. Orthomartingale-coboundary decomposition for stationary random fields. Stochastics and Dynamics, 2016, 16 (5). ⟨hal-01073516v2⟩