Orthomartingale-coboundary decomposition for stationary random fields

Mohamed El Machkouri; Davide Giraudo

doi:10.1142/s0219493716500179

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arXiv · 1410.3062

Orthomartingale-coboundary decomposition for stationary random fields

Mohamed El Machkouri·Davide Giraudo

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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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BibTeX RIS

Mohamed El Machkouri, Davide Giraudo. 2014-10-12. Orthomartingale-coboundary decomposition for stationary random fields. https://doi.org/10.1142/s0219493716500179

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