The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences

Suppose that X1, X2, … is some stationary zero mean Gaussian sequence with unit variance. Let {kn} be a certain nondecreasing sequence of positive integers, denote the kn largest maximum of X1, … Xn. We aim at proving the almost sure central limit theorems for the suitably normalized sequence under certain additional assumptions on {kn} and the covariance function .