Strong Local Nondeterminism and Exact Modulus of Continuity for Isotropic Gaussian Random Fields on Compact Two-Point Homogeneous Spaces

Tianshi Lu (), Chunsheng Ma () and Yimin Xiao ()
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Tianshi Lu: Wichita State University
Chunsheng Ma: Wichita State University
Yimin Xiao: Michigan State University

Journal of Theoretical Probability, 2023, vol. 36, issue 4, 2403-2425

Abstract: 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.

Keywords: Isotropy; Jacobi polynomial; Strong local nondeterminism; Uniform modulus of continuity; 60G60; 60G17; 60G15; 42C40 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01231-8

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