Some Generalizations of Gneiting's Univariate and Bivariate Models

Prof. Dr. Martin Schlather Institut für Mathematik Universität Mannheim (joint work with Olga Moreva & NIklas Hansen)

Gaussian random fields are completely characterized by their mean and their covariance function. In applications suitable classes of parametrized covariance functions are needed. Whilst in the univariate case a large number of classes is available, not that many classes exist in the multivariate case. In this talk we mainly focus on bivariate covariance functios that are generalizations or modifications of models that have been suggested by Tilmann Gneiting. In particular, the univariate cutoff embedding technique is transferred to the bivariate case. On that way, the results for the univariate case had to improved. As examples for the bivariate cutoff technique, we consider Gneiting's bivariate Matern model and modifications thereof. Finally, we show that Gneiting's generalized Cauchy model can be combined with the fractional Browian motion to get a parametric model that covers both the stationary and the intrinsically stationary case.