Random fields and their wavelet transforms and representation: covariance and spectral properties

The covariance and spectral properties of the wavelet transform and of the discrete wavelet coefficients, in the orthonormal series representation, of second-order random fields on Rⁿ are determined. Both weakly homogeneous random fields as well as random fields with weakly homogeneous increments are considered. Weakly isotropic fields and fields with weakly isotropic increments are also considered. Applications to fractional Brownian fields on Rⁿ are given