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This article is cited in 1 scientific paper (total in 1 paper)
On the exact asymptotics of small deviations of $L_2$-norm for some Gaussian random fields
L. V. Rozovskii Saint-Petersburg Chemical-Pharmaceutical Academy
Abstract:
In this paper we study the asymptotic behavior of the
tail probability $\mathbf P(V^2<r)$
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, $L_2$-norm.
Received: 18.03.2017 Revised: 08.11.2017 Accepted: 22.11.2017
Citation:
L. V. Rozovskii, “On the exact asymptotics of small deviations of $L_2$-norm for some Gaussian random fields”, Teor. Veroyatnost. i Primenen., 63:3 (2018), 468–481; Theory Probab. Appl., 63:3 (2019), 381–392
Linking options:
https://www.mathnet.ru/eng/tvp5140https://doi.org/10.4213/tvp5140 https://www.mathnet.ru/eng/tvp/v63/i3/p468
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