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Extremes of Gaussian processes with smooth random expectation and smooth random variance

Abstract

Let ξ(t), t ∈ [0, T],T > 0, be a Gaussian stationary process with expectation 0 and variance 1, and let η(t) and μ(t) be other sufficiently smooth random processes independent of ξ(t). In this paper, we obtain an asymptotic exact result for P(sup t∈[0,T](η(t)ξ(t) + μ(t)) > u) as u→∞.

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Correspondence to Vladimir Piterbarg.

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Piterbarg, V., Popivoda, G. & Stamatović, S. Extremes of Gaussian processes with smooth random expectation and smooth random variance. Lith Math J 57, 128–141 (2017). https://doi.org/10.1007/s10986-017-9347-2

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  • DOI: https://doi.org/10.1007/s10986-017-9347-2

MSC

  • 60G15
  • 60G70

Keywords

  • conditionally Gaussian process
  • Gaussian process
  • stationary random process
  • random expectation
  • random variance