Geodesic
Excursions of a Gaussian process with variable variance above a barrier increasing to infinity
Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 386-394 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a family of real-valued Gaussian processes $\xi_u(t)$, $t\in[0,T]$, we obtain an exact asymptotics of the probability of crossing a level $u$ as $u\to\infty$ under certain conditions on the variance and correlation. This result is applied to the investigation of excursions of a stationary zero-mean process above a barrier increasing to infinity.
Keywords: Gaussian process, excursions of Gaussian processes, level-crossing probability, fractional Brownian motion, covariance function. 
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S. G. Kobel'kov. Excursions of a Gaussian process with variable variance above a barrier increasing to infinity. Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 386-394. http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a7/

[1] V. I. Piterbarg, Asimptoticheskie metody v teorii gaussovskikh sluchainykh protsessov i polei, Izd-vo MGU, M., 1988 | Zbl

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

[3] V. I. Piterbarg, V. Prisyazhnyuk, “Asimptoticheskoe povedenie veroyatnosti bolshogo vybrosa dlya nestatsionarnogo gaussovskogo protsessa”, Teoriya veroyatn. i matem. statistika, 18 (1978), 121–134 | MR | Zbl

[4] M. R. Leadbetter, “On crossings of arbitrary curves by certain Gaussian processes”, Proc. Amer. Math. Soc., 16 (1965), 60–68 | DOI | MR | Zbl

[5] S. Berman, “Vybrosy statsionarnogo gaussovskogo protsessa za vysokii dvizhuschiisya barer”, Sluchainye protsessy. Vyborochnye funktsii i peresecheniya, Mir, M., 1978, 133–164 | MR | Zbl

[6] V. Piterbarg, O. Seleznjev, Linear interpolation of random processes and extremes of a sequence of Gaussian non-stationary processes, Proc. Tech. Rep., 446, North Carolina Univ., Chapel Hill, Center Stoch., 1994

[7] J. Hüsler, V. Piterbarg, O. Seleznev, “On convergence of the uniform norms for Gaussian processes and linear approximation problems”, Ann. Appl. Probab., 13:4 (2003), 1615–1653 | DOI | MR | Zbl

[8] E. Hashorva, J. Husler, “Extremes of Gaussian processes with maximal variance near the boundary points”, Methodol. Comput. Appl. Probab., 2:3 (2000), 255–269 | DOI | MR | Zbl