Some covariance models based on normal scale mixtures

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.