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 $u\rightarrow\infty$. 
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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/

[1] Belyaev Yu. K., Nosko V. P., “Kharakteristiki vybrosov za vysokii uroven gaussovskogo protsessa i ego ogibayuschei”, Teoriya veroyatn. i ee primen., 14:2 (1969), 302–314

[2] Nosko V. P., “Lokalnaya struktura odnorodnogo gaussovskogo sluchainogo polya v okrestnosti tochek vysokogo urovnya”, Teoriya veroyatn. i ee primen., 30:4 (1985), 722–736 | MR

[3] Nosko V. P., “Asimptoticheskie raspredeleniya kharakteristik vybrosov odnorodnogo gaussovskogo sluchainogo polya za vysokii uroven”, Teoriya veroyatn. i ee primen., 32:4 (1987), 722–733 | MR

[4] Leadbetter M. R., Lindgren G., Rootzen H., Extremes and Related Properties of Random Sequences and Processes, Springer, Berlin, 1983 | MR | Zbl

[5] Lindgren G., “Some properties of a normal process near a local maximum”, Ann. Math. Stat., 41 (1971), 1870–1883 | DOI | MR

[6] Pickands J., “Upcrossing probabilities for stationary Gaussian processes”, Trans. Am. Math. Soc., 145 (1969), 51–73 | DOI | MR | Zbl

[7] Piterbarg V. I., Asymptotic Methods in the Theory of Gaussian Processes and Fields, Transl. Math. Monogr., Amer. Math. Soc., Providence, 1996 | MR