Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure

Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transformation to GFGCC and GSGCC are studied.Gaussian field with generalized Cauchy covariance Gaussian sheet with generalized Cauchy covariance Self-similarity Long/short range dependence Lamperti transform