Limit Laws for Extremes of a Class of Gaussian Sequences

Abstract:

      In this paper, we discuss the extremes of a class of nonstationary Gaussian sequences. We apply the convergence theorem of the point process theory to obtain the convergence of the point process of more level's exceedances. Moreover, the asymptotic distribution of the maxima in disjoint intervals is obtained. The asymptotic distribution of $k$-th largest maxima and the asymptotic joint distribution for a finite number of the $r$th largest maxima are also obtained.