Time Varying Isotropic Vector Random Fields on Spheres

TL;DR

This paper develops a new series representation for time-varying isotropic vector random fields on spheres, aiding modeling and simulation, and introduces semiparametric models for such fields.

Contribution

It derives a general covariance matrix function and a novel series representation involving ultraspherical polynomials for these vector fields.

Findings

Provides a new series representation useful for modeling and simulation

Derives a general form of the covariance matrix function

Illustrates semiparametric models for vector fields

Abstract

For a vector random field that is isotropic and mean square continuous on a sphere and stationary on a temporal domain, this paper derives a general form of its covariance matrix function and provides a series representation for the random field, which involve the ultraspherical polynomials. The series representation is somehow an imitator of the covariance matrix function, but differs from the the spectral representation in terms of the ordinary spherical harmonics, and is useful for modeling and simulation. Some semiparametric models are also illustrated.