Characterization theorems for some classes of covariance functions associated to vector valued random fields

We characterize some important classes of cross-covariance functions associated to vector valued random fields based on latent dimensions. We also give some results for mixture based models that allow for the construction of new cross-covariance models. In particular, we give a criterion for the permissibility of quasi-arithmetic operators in order to construct valid cross covariances. (C) 2011 Elsevier Inc. All rights reserved.