Strong Law of Large Numbers for Functionals of Random Fields With Unboundedly Increasing Covariances

TL;DR

This paper establishes the Strong Law of Large Numbers for integral functionals of non-stationary random fields with unbounded covariances, covering cases with increasing domain size and long-range dependence.

Contribution

It provides new conditions under which the Strong Law of Large Numbers holds for a broad class of non-stationary random fields with unbounded covariances.

Findings

Proved SLLN for random fields with unbounded covariances.

Extended results to weak and long-range dependent fields.

Included numerical examples demonstrating applicability.

Abstract

The paper proves the Strong Law of Large Numbers for integral functionals of random fields with unboundedly increasing covariances. The case of functional data and increasing domain asymptotics is studied. Conditions to guarantee that the Strong Law of Large Numbers holds true are provided. The considered scenarios include wide classes of non-stationary random fields. The discussion about application to weak and long-range dependent random fields and numerical examples are given.