Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 3, pp. 480-495
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V. I. Piterbarg; V. P. Prisyažnuk. The exact asymptotics for the probability of large span of a Gaussian stationary process. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 3, pp. 480-495. http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a2/
@article{TVP_1981_26_3_a2,
author = {V. I. Piterbarg and V. P. Prisya\v{z}nuk},
title = {The exact asymptotics for the probability of large span of {a~Gaussian} stationary process},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {480--495},
year = {1981},
volume = {26},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a2/}
}
TY - JOUR
AU - V. I. Piterbarg
AU - V. P. Prisyažnuk
TI - The exact asymptotics for the probability of large span of a Gaussian stationary process
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1981
SP - 480
EP - 495
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a2/
LA - ru
ID - TVP_1981_26_3_a2
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%A V. I. Piterbarg
%A V. P. Prisyažnuk
%T The exact asymptotics for the probability of large span of a Gaussian stationary process
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1981
%P 480-495
%V 26
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a2/
%G ru
%F TVP_1981_26_3_a2
We obtain the exact asymptotics for the probability $$ \mathbf P\{\max_{0\le t\le 1}\xi_t-\min_{0\le t\le 1}\xi_t>u\},\qquad u\to\infty, $$ under the assumption that the correlation function of a Gaussian stationary process $\xi_t$, $t\in[0,1]$, varies regularly at the origin.
