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 involves Jacobi polynomials and the distance defined on the compact two-point homogeneous space.
Highlights
Consider the sphere Sd embedded into Rd+1 as follows: Sd = { x ∈ Rd+1 : x = 1 }, and define the distance between the points x1 and x2 by ρ(x1, x2) = cos−1(x1 x2)
It is natural to norm the distance in such a way that the length of any geodesic line is equal to 2π, exactly as in the case of the unit sphere
There is a trick that allows us to write down all zonal spherical functions of all compact two-point homogeneous spaces in the same form, which is used in probabilistic literature [2,26,28,29,33] and in approximation theory [9,13]
Summary
A series representation are derived in [24] for a vector random field that is isotropic and mean square continuous on a sphere and stationary on a temporal domain. They are extended to Md × T in this paper.
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