Spherically Invariant Vector Random Fields in Space and Time

This paper is concerned with spherically invariant or elliptically contoured vector random fields in space and/or time, which are formulated as scale mixtures of vector Gaussian random fields. While a spherically invariant vector random field may or may not have second-order moments, a spherically invariant second-order vector random field is determined by its mean and covariance matrix functions, just like the Gaussian one. This paper explores basic properties of spherically invariant second-order vector random fields, and proposes an efficient approach to develop covariance matrix functions for such vector random fields.