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
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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.
Mots-clés : $L_2$-norm.
@article{TVP_2018_63_3_a3,
author = {L. V. Rozovskii},
title = {On the exact asymptotics of small deviations of $L_2$-norm for some {Gaussian} random fields},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {468--481},
publisher = {mathdoc},
volume = {63},
number = {3},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a3/}
}
TY - JOUR AU - L. V. Rozovskii TI - On the exact asymptotics of small deviations of $L_2$-norm for some Gaussian random fields JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2018 SP - 468 EP - 481 VL - 63 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a3/ LA - ru ID - TVP_2018_63_3_a3 ER -
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/