Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces

TL;DR

This paper develops a mathematical framework for modeling time-varying isotropic vector random fields on compact two-point homogeneous spaces, providing covariance structures and series representations involving Jacobi polynomials.

Contribution

It introduces a general covariance matrix form and a series representation for vector random fields on these spaces, extending existing models to include temporal dynamics.

Findings

Derived a general covariance matrix function for such fields

Presented a series representation involving Jacobi polynomials

Extended models to include temporal stationarity

Abstract

A general form of the covariance matrix function is derived in this paper for a vector random field that is isotropic and mean square continuous on a compact connected two-point homogeneous space and stationary on a temporal domain. A series representation is presented for such a vector random field, which involve Jacobi polynomials and the distance defined on the compact two-point homogeneous space.