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Extremes of the time-average of stationary Gaussian processes. (English) Zbl 1227.60045
The authors establish an expansion of P\((\sup_{t\geq 0}I_Z(t)>u)\), as \(u\to\infty\), where \(I_Z(t)=t^{-1}\int_0^t Z(s)\,ds\) for \(t>0\) and \(I_Z(0)=Z(0)\) and \((Z(t))_{t\geq 0}\) is a centered stationary Gaussian process with covariance function satisfying some regularity conditions.
As an application, the probability of buffer emptiness in a Gaussian fluid queueing system and the collision probability of differentiable Gaussian processes with stationary increments are analyzed.

60G15 Gaussian processes
60G70 Extreme value theory; extremal stochastic processes
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
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