Probabilities of high extremes for a Gaussian stationary process in a random environment
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2017), pp. 11-16
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Let $\xi\left(t\right)$ be a zero-mean stationary Gaussian process with the covariance function $r\left(t\right)$ of Pickands type, i.e., $r(t)=1-|t|^{\alpha}+o(|t|^{\alpha}),~t\to 0,~0<\alpha\leq2$, and $\eta\left(t\right), \zeta\left(t\right)$ be periodic random processes. For any $T>0$ and independent $\xi\left(t\right)$, $\eta\left(t\right)$, $\zeta\left(t\right)$ we obtain the exact asymptotic behaviour of the probabilities $P(\max_{t\in[0,T]} \eta\left(t\right) \xi\left(t\right) > u)$, $P(\max_{t\in[0,T]} \left(\xi\left(t\right) + \eta\left(t\right)\right) > u)$ and $P(\max_{t\in[0,T]} \left(\eta\left(t\right) \xi\left(t\right) + \zeta\left(t\right)\right) > u)$ for $u \to \infty$.
@article{VMUMM_2017_1_a1,
author = {A. O. Kleban and M. V. Korulin},
title = {Probabilities of high extremes for a {Gaussian} stationary process in a random environment},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {11--16},
year = {2017},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2017_1_a1/}
}
TY - JOUR AU - A. O. Kleban AU - M. V. Korulin TI - Probabilities of high extremes for a Gaussian stationary process in a random environment JO - Vestnik Moskovskogo universiteta. Matematika, mehanika PY - 2017 SP - 11 EP - 16 IS - 1 UR - http://geodesic.mathdoc.fr/item/VMUMM_2017_1_a1/ LA - ru ID - VMUMM_2017_1_a1 ER -
%0 Journal Article %A A. O. Kleban %A M. V. Korulin %T Probabilities of high extremes for a Gaussian stationary process in a random environment %J Vestnik Moskovskogo universiteta. Matematika, mehanika %D 2017 %P 11-16 %N 1 %U http://geodesic.mathdoc.fr/item/VMUMM_2017_1_a1/ %G ru %F VMUMM_2017_1_a1
A. O. Kleban; M. V. Korulin. Probabilities of high extremes for a Gaussian stationary process in a random environment. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2017), pp. 11-16. http://geodesic.mathdoc.fr/item/VMUMM_2017_1_a1/
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