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

Xiaohong Lan, Domenico Marinucci and Yimin Xiao

Stochastic Processes and their Applications, 2018, vol. 128, issue 4, 1294-1315

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.

Keywords: Spherical Gaussian fields; Strong local nondeterminism; Uniform modulus of continuity; Spherical wavelets (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spa.2017.07.008

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