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

Abstract

Let X 1 , X 2 , . . . 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 Choi (2010) and Csáki and Gonchigdanzan (2002).Keywords: stationary standardized Gaussian random fieldsmaximaalmost sure central limit theorem.2000 MSC: 60F15.

Almost sure limit theorem for the order statistics of stationary Gaussian sequences

“…Csáki and Gonchigdanzan (2002) showed that condition (3) is enough for (1). For more work on this topic, we refer to Chen and Lin (2006) and Peng and Nadarajah (2011) for the non-stationary Gaussian case, Tan (2013) for continuous time Gaussian process, Tan and Wang (2014) and Wu (2017) for Gaussian random field. It is also of interest to extend (1) to order statistics.…”