Geodesic
High level exceeding probability for a Gaussian process with constant variance and variable smoothness
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2024), pp. 21-25
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Exact asymptotic behavior is evaluated for high level exceeding probability of Gaussian process with constant variance, the correlation function of which satisfies the Pickands' condition at each point, while the constants in the condition change, being continuous functions. 
@article{VMUMM_2024_4_a2,
     author = {Ph. E. Koluzanov and V. I. Piterbarg},
     title = {High level exceeding probability for a {Gaussian} process with constant variance and variable smoothness},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {21--25},
     year = {2024},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2024_4_a2/}
}
TY  - JOUR
AU  - Ph. E. Koluzanov
AU  - V. I. Piterbarg
TI  - High level exceeding probability for a Gaussian process with constant variance and variable smoothness
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2024
SP  - 21
EP  - 25
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2024_4_a2/
LA  - ru
ID  - VMUMM_2024_4_a2
ER  - 
%0 Journal Article
%A Ph. E. Koluzanov
%A V. I. Piterbarg
%T High level exceeding probability for a Gaussian process with constant variance and variable smoothness
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2024
%P 21-25
%N 4
%U http://geodesic.mathdoc.fr/item/VMUMM_2024_4_a2/
%G ru
%F VMUMM_2024_4_a2
Ph. E. Koluzanov; V. I. Piterbarg. High level exceeding probability for a Gaussian process with constant variance and variable smoothness. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2024), pp. 21-25. http://geodesic.mathdoc.fr/item/VMUMM_2024_4_a2/

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

[2] Piterbarg V.I., “O rabote Pikandsa “Veroyatnosti peresecheniya dlya gaussovskogo statsionarnogo protsessa””, Vestn. Mosk. un-ta. Matem. Mekhan., 1972, no. 5, 5–30 | Zbl

[3] Husler J., “Extreme values and high boundary crossings of locally stationary Gaussian processes”, Ann. Probab., 18:3 (1990), 1141–1158 | DOI | MR | Zbl

[4] Kobelkov S.G., Piterbarg V.I., Rodionov I. V., Khashorva E., “Veroyatnost vysokogo maksimuma traektorii gaussovskogo nestatsionarnogo protsessa”, Fund. i prikl. matem., 23:1 (2020), 161–174

[5] Kobelkov S.G., Piterbarg V.I., “On maximum of Gaussian random field having unique maximum point of its variance”, Extremes, 22:4 (2019), 413–432 | DOI | MR | Zbl

[6] Piterbarg V.I., Dvadtsat lektsii o gaussovskikh protsessakh, MTsNMO, M., 2020

[7] Piterbarg V.I., Asymptotic Methods in Theory of Gaussian Random Processes and Fields, Translations of Mathematical Monographes, 148, Amer. Math. Soc., Providence, 2012 | DOI | MR

[8] Qiao Wanli, “Extremes of locally stationary Gaussian and chi fields on manifolds”, Stochast. Process and Appl., 133 (2021), 166–192 \bf 133(C) | DOI | MR | Zbl

[9] Debicki K., “Some properties of generalized Pickands constant”, Teor. veroyatn. i ee primen., 50:2 (2005), 396–404 | DOI | MR

[10] Fedoryuk M.V., Metod perevala, Nauka, M., 1977