Strong Gaussian approximation of an associated random field. (English. Russian original) Zbl 1143.60026

Shashkin, A. P.

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.

Reviewer: Michael Högele (Berlin)

MSC:

60F15	Strong limit theorems
60G60	Random fields
60G15	Gaussian processes

Keywords:

associated random field; strong invariance principle; strong Gaussian approximation; Cox-Grimmet coefficients of polynomial decay