Interpolation of homogeneous and isotropic random field in the center of the sphere by uniform distributed observations

Abstract

We consider interpolation of homogeneous and isotropic random field in the center of the sphere by uniform distributed observations on the sphere. The asymptotic behavior of the mean-square interpolation error is investigated. The degree of convergence to zero of the meansquare interpolation error is obtained. Efficient volume of the set of observations is given.