Uniform Modulus of Continuity of Random Fields

TL;DR

This paper establishes a sufficient condition for the uniform modulus of continuity of random fields, including those with heavy-tailed distributions like stable fields, enhancing understanding of their regularity properties.

Contribution

It introduces a new sufficient condition for the uniform modulus of continuity applicable to a broad class of random fields, including heavy-tailed types.

Findings

Provides a sufficient condition for uniform continuity

Applicable to stable and heavy-tailed random fields

Enhances understanding of regularity in random fields

Abstract

A sufficient condition for the uniform modulus of continuity of a random field $X = \{X(t), t \in \R^N\}$ is provided. The result is applicable to random fields with heavy-tailed distribution such as stable random fields.