Strong Local Nondeterminism and Exact Modulus of Continuity for Spherical Gaussian Fields

TL;DR

This paper investigates the sample path properties of isotropic spherical Gaussian fields, establishing strong local nondeterminism and an exact modulus of continuity, and analyzing how spectral index influences fractal or smooth behavior.

Contribution

It introduces the property of strong local nondeterminism for spherical Gaussian fields and derives an exact modulus of continuity based on spectral properties.

Findings

Established strong local nondeterminism for spherical Gaussian fields

Derived exact uniform modulus of continuity for sample paths

Analyzed spectral index range for fractal versus smooth behavior

Abstract

In this paper, we are concerned with sample path properties of isotropic spherical Gaussian fields on $\S^2$. In particular, we establish the property of strong local nondeterminism of an isotropic spherical Gaussian field based on the high-frequency behaviour of its angular power spectrum; we then exploit this result to establish an exact uniform modulus of continuity for its sample paths. We also discuss the range of values of the spectral index for which the sample functions exhibit fractal or smooth behaviour.