Geodesic
On the maximum of a Gaussian process with unique maximum point of its variance
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 1, pp. 161-174 
S. G. Kobelkov; V. I. Piterbarg; I. V. Rodionov; E. Hashorva. On the maximum of a Gaussian process with unique maximum point of its variance. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 1, pp. 161-174. http://geodesic.mathdoc.fr/item/FPM_2020_23_1_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Gaussian random processes whose variances reach their maximum values at unique points are considered. Exact asymptotic behavior of probabilities of large absolute maximums of their trajectories have been evaluated using the double sum method under the widest possible conditions.

[1] Piterbarg V. I., “O rabote Pikandsa «Veroyatnosti peresecheniya dlya gaussovskogo statsionarnogo protsessa»”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 5 (1972), 25–30 | Zbl

[2] Piterbarg V. I., Dvadtsat lektsii o gaussovskikh protsessakh, MTsNMO, M., 2015

[3] Piterbarg V. I., Prisyazhnyuk V. P., “Asimptotika veroyatnosti bolshogo vybrosa gaussovskogo nestatsionarnogo protsessa”, Teor. veroyatn. i matem. stat., 18 (1978), 121–134 | Zbl

[4] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 2, Mir, M., 1967 | MR

[5] Bingham N. H., Goldie C. M., Teugels J. L., Regular Variation, Cambridge Univ. Press, Cambridge, 1987 | MR | Zbl

[6] Dȩbicki K., Hashorva E., Liu P., “Extremes of Gaussian random fields with regularly varying dependence structure”, Extremes, 20 (2017), 333–392 | DOI | MR

[7] Geman D., Horowitz J., “Occupation densities”, Ann. Probab., 8:1 (1980), 1–67 | DOI | MR | Zbl

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

[9] Piterbarg V. I., Asymptotic Methods in Theory of Gaussian Random Processes and Fields, Transl. Math. Monogr., 148, Amer. Math. Soc., Providence, 2012 | DOI | MR

[10] Piterbarg V. I., Rodionov I. V., “High excursions of Bessel and related random processes”, Stoch. Proc. Appl., 130:8 (2020), 4859–4872 | DOI | MR | Zbl