| Let {ξ(t),t≥0} be a stationary Gaussian process with covariance function R(t) statisfying R(t) logt→ γ>0 as t→∞ and R(t)=1-c|t|αα+o(|t| α) as t→0 where 0<α≤2 and c>0 . In this paper, we establish the limit theorems of the point process of ε-upcrossings of one or more high levels by {ξ(t),t≥0} , and we obtain the limiting distributions of maxima and the joint asymptotic distributions of several local ε-maximas. |
