Orthomartingale-coboundary decomposition for stationary random fields

2014/10/12 by Mohamed El Machkouri, Davide Giraudo · 1 citation
Mathematics · #math.PR

paper · pdf · doi:10.1142/s0219493716500179

published as Stoch. Dyn. 16 (2016), no. 5, 1650017

arxiv created 2014/10/12 · arxiv updated 2017/04/28

Abstract

We provide a new projective condition for a stationary real random field indexed by the lattice \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.

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