Geodesic
On the shape of a high excursion of a Gaussian stationary process
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 3, pp. 119-125

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We investigate the shape of an excursion above a high level $u$ by a stationary Gaussian process. The shape depends on the conditioned mean and covariances of the underlying process. The paths vary slightly around a deterministic trend. The probability of such event can be determined asymptotically exactly for $u\rightarrow\infty$. 
@article{FPM_2018_22_3_a6,
     author = {E. V. Kremena},
     title = {On the shape of a high excursion of a {Gaussian} stationary process},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {119--125},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2018_22_3_a6/}
}
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E. V. Kremena. On the shape of a high excursion of a Gaussian stationary process. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 3, pp. 119-125. http://geodesic.mathdoc.fr/item/FPM_2018_22_3_a6/