Geodesic
On normal approximation for strongly mixing random fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 1, pp. 60-68 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we estimate the difference $|\mathbf Eh(Z_V)-\mathbf Eh(N)|$, where $Z_V$ is a sum over any finite subset $V$ of the standard lattice $\mathbf Z^d$ of normalized random variables of the strongly mixing random field $\{X_a,\ a\in\mathbf Z^d\}$ (without assuming stationarity) and $N$ is a standard normal random variable for the function $h\colon\mathbf R\to\mathbf R$, which is finite and satisfies the Lipschitz condition. In a particular case, the obtained upper bounds of $|\mathbf Eh(Z_V)-\mathbf Eh(N)|$ in Theorems 3 and 4 are of order $O(|V|^{-1/2})$.
Keywords: normal approximations, bounded Lipschitz metrics, random fields, strong mixing condition, method of Stein. 
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J. Sunklodas. On normal approximation for strongly mixing random fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 1, pp. 60-68. http://geodesic.mathdoc.fr/item/TVP_2007_52_1_a3/

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