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High Excursions of Gaussian Nonstationary Processes in Discrete Time

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Abstract

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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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    I. A. Kozik & V. I. Piterbarg

Authors
  1. I. A. Kozik
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  2. V. I. Piterbarg
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Correspondence to I. A. Kozik.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 2, pp. 159–169, 2018.

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Kozik, I.A., Piterbarg, V.I. High Excursions of Gaussian Nonstationary Processes in Discrete Time. J Math Sci 253, 867–874 (2021). https://doi.org/10.1007/s10958-021-05276-8

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  • DOI: https://doi.org/10.1007/s10958-021-05276-8

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