Abstract

This paper focuses on vector random fields defined on S-d x R-k , d >= 2 and k >= 1, with covariance functions that depend on the geodesic distance in S-d and on the separation vector in R-k. First, we propose parametric families of nonseparable covariance functions with closed-form expressions and explicit spectral representations. Then, we derive an algorithm for fast simulation of such random fields, which combines spectral simulation methods in S-d and R-k previously introduced in the literature and relies on importance sampling techniques. We provide computer codes and practical guidelines and describe the advantages of our proposal in comparison to other methods.