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Strong local nondeterminism and exact modulus of continuity for spherical Gaussian fields

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  • Lan, Xiaohong
  • Marinucci, Domenico
  • Xiao, Yimin

Abstract

In this paper, we are concerned with sample path properties of isotropic spherical Gaussian fields on S2. 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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:4:p:1294-1315
    DOI: 10.1016/j.spa.2017.07.008
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    References listed on IDEAS

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    1. Lan, Xiaohong & Marinucci, Domenico, 2009. "On the dependence structure of wavelet coefficients for spherical random fields," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3749-3766, October.
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    Cited by:

    1. Bingham, Nicholas H. & Symons, Tasmin L., 2022. "Gaussian random fields on the sphere and sphere cross line," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 788-801.

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