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

Author

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  • Tianshi Lu

    (Wichita State University)

  • Chunsheng Ma

    (Wichita State University)

  • Yimin Xiao

    (Michigan State University)

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.

Suggested Citation

  • Tianshi Lu & Chunsheng Ma & Yimin Xiao, 2023. "Strong Local Nondeterminism and Exact Modulus of Continuity for Isotropic Gaussian Random Fields on Compact Two-Point Homogeneous Spaces," Journal of Theoretical Probability, Springer, vol. 36(4), pages 2403-2425, December.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:4:d:10.1007_s10959-022-01231-8
    DOI: 10.1007/s10959-022-01231-8
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    References listed on IDEAS

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    1. Chunsheng Ma, 2017. "Time Varying Isotropic Vector Random Fields on Spheres," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1763-1785, December.
    2. Lu, Tianshi & Du, Juan & Ma, Chunsheng, 2022. "Stochastic comparison for elliptically contoured random fields," Statistics & Probability Letters, Elsevier, vol. 189(C).
    3. Lan, Xiaohong & Xiao, Yimin, 2018. "Strong local nondeterminism of spherical fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 44-50.
    4. Lan, Xiaohong & Marinucci, Domenico & Xiao, Yimin, 2018. "Strong local nondeterminism and exact modulus of continuity for spherical Gaussian fields," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1294-1315.
    5. Tianshi Lu & Chunsheng Ma, 2020. "Isotropic Covariance Matrix Functions on Compact Two-Point Homogeneous Spaces," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1630-1656, September.
    6. Cleanthous, Galatia & Georgiadis, Athanasios G. & Lang, Annika & Porcu, Emilio, 2020. "Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4873-4891.
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    Cited by:

    1. Chunsheng Ma, 2024. "Bifractional Brownian Motions on Metric Spaces," Journal of Theoretical Probability, Springer, vol. 37(2), pages 1299-1332, June.

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