A note on the almost sure central limit theorems for the maxima of strongly dependent nonstationary Gaussian vector sequences

Abstract

We prove some almost sure central limit theorems for the maxima of strongly dependent nonstationary Gaussian vector sequences under some mild conditions. The results extend the ASCLT to nonstationary Gaussian vector sequences and give substantial improvements for the weight sequence obtained by Lin et al. (Comput. Math. Appl. 62(2):635-640, 2011). MSC: 60F15