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On the Shape of a High Excursion of a Gaussian Stationary Process

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Abstract

We investigate the shape of an excursion above a high level u by a stationary Gaussian process. The shape depends on the conditioned mean and covariances of the underlying process. The paths vary slightly around a deterministic trend. The probability of such event can be determined asymptotically exactly for u → ∞.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    E. V. Kremena

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  1. E. V. Kremena
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Correspondence to E. V. Kremena.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 3, pp. 119–125, 2018.

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Kremena, E.V. On the Shape of a High Excursion of a Gaussian Stationary Process. J Math Sci 254, 532–536 (2021). https://doi.org/10.1007/s10958-021-05323-4

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  • DOI: https://doi.org/10.1007/s10958-021-05323-4

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