Vector random fields with compactly supported covariance matrix functions

The objective of this paper is to construct covariance matrix functions whose entries are compactly supported, and to use them as building blocks to formulate other covariance matrix functions for second-order vector stochastic processes or random fields. In terms of the scale mixture of compactly supported covariance matrix functions, we derive a class of second-order vector stochastic processes on the real line whose direct and cross covariance functions are of Pólya type. Then some second-order vector random fields in RdRd whose direct and cross covariance functions are compactly supported are constructed by using a convolution approach and a mixture approach.