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Extremes of the time-average of stationary Gaussian processes

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  • De[combining cedilla]bicki, Krzysztof
  • Tabis, Kamil

Abstract

We study the exact asymptotics of , as u-->[infinity], where and {Z(t):t>=0} is a centered stationary Gaussian process with covariance function satisfying some regularity conditions. As an application, we analyze the probability of buffer emptiness in a Gaussian fluid queueing system and the collision probability of differentiable Gaussian processes with stationary increments. Additionally, we find estimates for analogues of Piterbarg-Prisyazhnyuk constants, that appear in the form of the considered asymptotics.

Suggested Citation

  • De[combining cedilla]bicki, Krzysztof & Tabis, Kamil, 2011. "Extremes of the time-average of stationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2049-2063, September.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:9:p:2049-2063
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    References listed on IDEAS

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    1. O'Connell, Neil & Unwin, Antony, 1992. "Collision times and exit times from cones: a duality," Stochastic Processes and their Applications, Elsevier, vol. 43(2), pages 291-301, December.
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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.

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