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

ABSTRACT

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) and Choi (2010).

KEYWORDS:

• Almost sure central limit theorem
• Maxima
• Stationary standardized Gaussian random fields.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F15

Acknowledgments

The author is very grateful to the referees and the editors for their valuable comments and some helpful suggestions that improved the clarity and readability of the article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (11361019 and 11661029). This project was supported by Program to Sponsor Teams for Innovation in the Construction of Talent Highlands in Guangxi Institutions of Higher Learning ([2011] 47) and the Support Program of the Guangxi China Science Foundation (2015GXNSFAA139008).