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Extremes of Gaussian processes with a smooth random variance


  • Hösler, Jörg
  • Piterbarg, Vladimir
  • Rumyantseva, Ekaterina


Let ξ(t) be a standard stationary Gaussian process with covariance function r(t), and η(t), another smooth random process. We consider the probabilities of exceedances of ξ(t)η(t) above a high level u occurring in an interval [0,T] with T>0. We present asymptotically exact results for the probability of such events under certain smoothness conditions of this process ξ(t)η(t), which is called the random variance process. We derive also a large deviation result for a general class of conditional Gaussian processes X(t) given a random element Y.

Suggested Citation

  • Hösler, Jörg & Piterbarg, Vladimir & Rumyantseva, Ekaterina, 2011. "Extremes of Gaussian processes with a smooth random variance," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2592-2605, November.
  • Handle: RePEc:eee:spapps:v:121:y:2011:i:11:p:2592-2605

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    Cited by:

    1. Tan, Zhongquan, 2013. "An almost sure limit theorem for the maxima of smooth stationary Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2135-2141.
    2. Popivoda, Goran & Stamatović, Siniša, 2016. "Extremes of Gaussian fields with a smooth random variance," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 185-190.


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