On the maxima of nonstationary random fields subject to missing observations

TL;DR

This paper investigates the asymptotic behavior of maxima in nonstationary random fields with missing data, providing convergence results and illustrating with Gaussian, chi, and order statistics fields.

Contribution

It introduces new limit theorems for maxima of nonstationary random fields with missing observations, extending previous work to broader classes of fields.

Findings

Weak convergence of maxima established

Almost sure convergence demonstrated

Results applicable to Gaussian, chi, and order statistics fields

Abstract

Motivated by the papers of Mladenovc and Piterbarg (2006), Krajka (2011) and Pereira and Tan (2017), we study the limit properties for the maxima from nonstationary 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.