Geodesic
High excursions of Gaussian nonstationary processes in discrete time
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 2, pp. 159-169

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Exact asymptotic behavior is given for high excursion probabilities of Gaussian processes in discrete time as the corresponding lattice pitch unboundedly decreases. The proximity of the asymptotic behavior to that in continuous time is discussed. Examples are given related to fractional Brownian motion and the corresponding ruin problem. 
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     author = {I. A. Kozik and V. I. Piterbarg},
     title = {High excursions of {Gaussian} nonstationary processes in discrete time},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {159--169},
     publisher = {mathdoc},
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     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2018_22_2_a9/}
}
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I. A. Kozik; V. I. Piterbarg. High excursions of Gaussian nonstationary processes in discrete time. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2018) no. 2, pp. 159-169. http://geodesic.mathdoc.fr/item/FPM_2018_22_2_a9/