  We derive the limiting distributions of exceedances point processes of
randomly scaled weakly dependent stationary Gaussian sequences under some mild
asymptotic conditions. In the literature analogous results are available only
for contracted stationary Gaussian sequences. In this paper, we include
additionally the case of randomly inflated stationary Gaussian sequences with a
Weibullian type random scaling. It turns out that the maxima and minima of both
contracted and inflated weakly dependent stationary Gaussian sequences are
asymptotically independent.
