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.

中文翻译：

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具有协方差无限增大的随机域泛函的强大数定律

摘要

本文证明了协方差无限增大的随机场积分函数的强大数定律。研究了功能数据和域渐近渐近的情况。提供了保证《大数定律》成立的条件。所考虑的场景包括广泛类别的非平稳随机字段。给出了关于弱和远距离相关随机场的应用的讨论，并给出了数值示例。