A Gneiting-like method for constructing positive definite functions on metric spaces [article]

V. S. Barbosa, V. A. Menegatto
2020 arXiv   pre-print
This paper is concerned with the construction of positive definite functions on a cartesian product of quasi-metric spaces using generalized Stieltjes and complete Bernstein functions. The results we prove are aligned with a well-established method of T. Gneiting to construct space-time positive definite functions and its many extensions. For the right choice of the quasi-metric spaces, the models discussed in the paper lead to flexible, interpretable and even computationally feasible classes
more » ... cross-covariance functions for multivariate random fields adopted in statistics. Necessary and sufficient conditions for the strict positive definiteness of the models are provided when the spaces are metric.
arXiv:2006.12217v1 fatcat:ceq545utmfbmbc6ienpz5ogus4