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a b s t r a c tWe 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.

We study functions introduced by Buhmann. The exact exponent of smoothness of these functions is obtained and the problem of positivity of their Hankel transforms is analyzed.

We characterize the Gneiting class of space-time covariance functions and give more relaxed conditions on the functions involved. We then show necessary conditions for the construction of compactly supported functions of the Gneiting type. These conditions are very general since they do not depend on the Euclidean norm.

No abstract