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Strong Gaussian approximation of an associated random field. (English. Russian original) Zbl 1143.60026
Russ. Math. Surv. 62, No. 5, 1012-1014 (2007); translation from Usp. Mat. Nauk 62, No. 5, 171-172 (2007).
In these communications the author states a strong invariance principle for wide-sense stationary associated random fields over a grid which are uniformly in \(L^p\), \(p>2\) , where the respective Cox-Grimmet coefficients have to decrease of polynomial order. The techniques of proof depend two lemmata which rely on a theorem about functions of associated vectors, further on Sentatov’s inequality for the Lévy-Prochorov metric and Strassen’s theorem on this respect.
MSC:
60F15 Strong limit theorems
60G60 Random fields
60G15 Gaussian processes
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