Strong Law of Large Numbers for Functionals of Random Fields With Unboundedly Increasing Covariances
Probability
2020-11-11 v1 Statistics Theory
Statistics Theory
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.
Keywords
Cite
@article{arxiv.2011.04874,
title = {Strong Law of Large Numbers for Functionals of Random Fields With Unboundedly Increasing Covariances},
author = {Illia Donhauzer and Andriy Olenko and Andrei Volodin},
journal= {arXiv preprint arXiv:2011.04874},
year = {2020}
}
Comments
21 pages, 4 figures