An asymptotic estimate of the probability for a Gaussian stochastic process to remain under the straight line $kt+a$

A stationary Gaussian stochastic process with the correlation function of the form (1) or (6) for $\tau\sim+0$ is considered, asymptotic inequalities (theorems 1–6) for the function (2) with $\alpha\sim+0$, $a\ge0$ or $\gamma_0\to+\infty$, $\alpha=\mathrm{const}$ (cf. (3)) being obtained.