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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.

##### MSC:
 60G15 Gaussian processes 60G70 Extreme value theory; extremal stochastic processes 68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
##### Keywords:
extremes; time-average; stationary Gaussian process
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##### References:
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