Regularity properties and simulations of Gaussian random fields on the Sphere cross Time

2016/11/09 by de La Cerda, Jorge Clarke, Alegría, Alfredo, Porcu, Emilio +1
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1611.02851

Abstract

We study the regularity properties of Gaussian fields defined over spheres cross time. In particular, we consider two alternative spectral decompositions for a Gaussian field on \mathbbS^d × ℝ. For each decomposition, we establish regularity properties through Sobolev and interpolation spaces. We then propose a simulation method and study its level of accuracy in the L² sense. The method turns to be both fast and efficient.

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