Orthomartingale-coboundary decomposition for stationary random fields. (English) Zbl 1346.60069
Summary: 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 R. Cairoli [C. R. Acad. Sci., Paris, Sér. A 269, 587–589 (1969; Zbl 0181.44201)]. Our main result can be viewed as a multidimensional version of the martingale-coboundary decomposition method, the idea of which goes back to M. I. Gordin [Sov. Math., Dokl. 10, 1174–1176 (1969); translation from Dokl. Akad. Nauk SSSR 188, 739–741 (1969; Zbl 0212.50005)]. 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.
MSC:
| 60G60 | Random fields |
| 60G48 | Generalizations of martingales |
| 60G10 | Stationary stochastic processes |
| 60F10 | Large deviations |
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