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We derive the limiting distributions of exceedances point processes ofrandomly scaled weakly dependent stationary Gaussian sequences under some mildasymptotic conditions. In the literature analogous results are available onlyfor contracted stationary Gaussian sequences. In this paper, we includeadditionally the case of randomly inflated stationary Gaussian sequences with aWeibullian type random scaling. It turns out that the maxima and minima of bothcontracted and inflated weakly dependent stationary Gaussian sequences areasymptotically independent.

Limit properties of exceedances point processes of scaled stationary Gaussian sequences