The exact asymptotics for the probability of large span of a Gaussian stationary process

We obtain the exact asymptotics for the probability
$$ \mathbf P\{\max_{0\le t\le 1}\xi_t-\min_{0\le t\le 1}\xi_t>u\},\qquad u\to\infty, $$
under the assumption that the correlation function of a Gaussian stationary process $\xi_t$, $t\in[0,1]$, varies regularly at the origin.