Series representations of isotropic vector random fields on balls

Abstract

This paper deals with a class of second-order vector random fields in the unit ball of Rd, whose direct/cross covariances are invariant or isotropic with respect to a distance defined on the ball, and gives a series representation of such an isotropic vector random field. A necessary format of covariance matrix functions is also derived for isotropic and mean square continuous vector random fields on the ball.