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

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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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     author = {S. G. Kobel'kov},
     title = {Excursions of a {Gaussian} process with variable variance above a barrier increasing to infinity},
     journal = {Matemati\v{c}eskie zametki},
     pages = {386--394},
     publisher = {mathdoc},
     volume = {80},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a7/}
}
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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/