  Modelling spatio-temporal processes has become an important issue in current
research. Since Gaussian processes are essentially determined by their second
order structure, broad classes of covariance functions are of interest. Here, a
new class is described that merges and generalizes various models presented in
the literature, in particular models in Gneiting (J. Amer. Statist. Assoc. 97
(2002) 590--600) and Stein (Nonstationary spatial covariance functions (2005)
Univ. Chicago). Furthermore, new models and a multivariate extension are
introduced.
