K-distributed vector random fields in space and time

Abstract

This paper introduces two types of second-order vector random fields or stochastic processes whose marginals are K-distributed, through certain mixture procedures. The first type is formulated as an independent product of a Gamma random variable and a χ2 vector random field, with an arbitrary spatial, temporal, or spatio-temporal index domain. The second type is formed as an independent product of a Gamma process and a χ2 vector random field, with the index domain limited on the nonnegative part of the real line. We derive the mean and covariance matrix functions of these K-distributed vector random fields, as well as the corresponding finite-dimensional Laplace transformations.