An extension of almost sure central limit theorem for the maximum of stationary Gaussian random fields

Let X₁, X₂, … be a sequence of stationary standardized Gaussian random fields. The almost sure limit theorem for the maxima of stationary Gaussian random fields is established. Our results extend and improve the results in Csáki and Gonchigdanzan (2002 Csáki, E., Gonchigdanzan, K. (2002). Almost sure limit theorems for the maximum of stationary Gaussian sequences. Stat. Probab. Lett. 58:195–203.Crossref], Web of Science ®] , Google Scholar]) and Choi (2010 Choi, H. (2010). Almost sure limit theorem for stationary Gaussian random fields. J. Korean Stat. Soc. 39:449–454.Crossref], Web of Science ®] , Google Scholar]).