Lithuanian Mathematical Journal

, Volume 57, Issue 1, pp 128–141 | Cite as

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

  • Vladimir Piterbarg
  • Goran Popivoda
  • Siniša Stamatović
Article
  • 35 Downloads

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→∞.

Keywords

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

MSC

60G15 60G70 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Vladimir Piterbarg
    • 1
  • Goran Popivoda
    • 2
  • Siniša Stamatović
    • 2
  1. 1.Moscow Lomonosov State UniversityMoscowRussia
  2. 2.University of MontenegroPodgoricaMontenegro

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