Geodesic
On the exact asymptotics of small deviations of $L_2$-norm for some Gaussian random fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 468-481 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we study the asymptotic behavior of the tail probability $\mathbf P(V^2 as $r\to 0$, where the sum $V^2$ is given by the formula $V^2=a^2 \sum_{i,j\ge 1} (i+\beta)^{-2c}(j+\delta)^{-2}\xi^2_{ij}$. Here $\{\xi_{ij}\}$ are independent standard Gaussian random variables, and $a>0$, $\beta >-1$, $\delta>-1$, $c>1/2$, $\ne 1$ are some constants. Thus, we study small deviations of the $L_2$-norm of certain two-parameter Gaussian random fields, that have the structure of a tensor product.
Keywords: small deviations, Karhunen–Loève expansion, Gaussian random field, tensor product
Mots-clés : $L_2$-norm. 
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L. V. Rozovskii. On the exact asymptotics of small deviations of $L_2$-norm for some Gaussian random fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 468-481. http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a3/

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