On the maxima of non stationary random fields subject to missing observations

Abstract

Motivated by the papers of Mladenović and Piterbarg (2006), Krajka (2011), and Pereira and Tan (2017), we study the limit properties for the maxima from non stationary random fields subject to missing observations and obtain the weakly convergence and almost sure convergence results for these maxima. Some examples such as Gaussian random fields, chi-random fields, and Gaussian order statistics fields are given to illustrate the obtained results.

KEYWORDS:

• Extreme value theory
• non stationary random fields
• missing observations
• almost sure central limit theorem

AMS Classification:

• Primary 60G70
• Secondary 60G60

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

Research supported by Innovation of Jiaxing City: a program to support the talented persons, National Bureau of Statistics of China (No. 2020LY031) and Project of new economy research center of Jiaxing City (No. WYZB202254, WYZB202257).