Cubature and Reconstruction of Smooth Isotropic Random Functions

We propose isotropic probability measures deened on classes of smooth multivariate functions. These provide a natural extension of the classical isotropic Wiener measure to multivariate functions from C 2r. We show that in the corresponding average case setting the minimal errors of algorithms that use n function values are ? n ?(d+4r+1)=2d and ? n ?(4r+1… (More)