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ͳƨO Gaussian Random Fields on the Sphere: Some Probabilistic and Statistical Properties

༭wfy ʱ䣺20191129 ʴ:144

}Ŀ Gaussian Random Fields on the Sphere: Some Probabilistic and Statistical Properties

ˣ Professor Y.M. Xiao, Michigan State University

rg 20191219գģ15: 30

c 㽭WȪУ^Wꖘ316

ժҪ  Let T(x), x\in S^2 be a real-valued Gaussian random field,  where  S^2 is the unit sphere in R^3. This talk is concerned with probabilistic and statistical properties of T. When T is isotropic, we show that many properties of T(x) such as regularity, geometric properties of the sample function xT(x)  are explicitly determined by the high-frequency behavior of its angular power spectrum.

Moreover, optimal bounds for the prediction errors of the spherical Gaussian field T are derived.

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