Strong local nondeterminism and exact modulus of continuity for isotropic Gaussian random fields on compact two-point homogeneous spaces

Abstract

This paper is concerned with sample path properties of real-valued isotropic Gaussian fields on compact two-point homogeneous spaces. In particular, we establish the property of strong local nondeterminism of an isotropic Gaussian field and then exploit this result to establish an exact uniform modulus of continuity for its sample paths.