We study separable mean zero Gaussian processes $X(t)$ with correlation ρ (t, s) for which 1 - ρ (t, s) is asymptotic to a regularly varying (at zero) function of $|t - s|$ with exponent 0 < α 2. For such processes, we obtain the asymptotic distribution of the maximum of $X(t)$. This result is used to obtain a result for $X(t)$ as t → ∞ similar to the so-called law of the iterated logarithm.
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Qualls et al. (1972) studied this question.