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

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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.

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Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

The authors thank the two anonymous referees for their careful reading of the previous version of the manuscript and for their constructive comments that have helped us to improve our paper significantly.The research of Y. Xiao is supported in part by the NSF grant DMS-1855185. The research of T. Lu is supported in part by the Wichita State University Convergence Sciences Initiative Program.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas, 67260-0033, USA

    Tianshi Lu & Chunsheng Ma

  2. Department of Statistics and Probability, Michigan State University, East Lansing, Michigan, 48824, USA

    Yimin Xiao

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  1. Tianshi Lu
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Correspondence to Tianshi Lu.

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Lu, T., Ma, C. & Xiao, Y. Strong Local Nondeterminism and Exact Modulus of Continuity for Isotropic Gaussian Random Fields on Compact Two-Point Homogeneous Spaces. J Theor Probab 36, 2403–2425 (2023). https://doi.org/10.1007/s10959-022-01231-8

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