Monday, June 07, 2021, 17:00
In geostatistical analysis, we are faced with the formidable challenge of specifying a valid spatio-temporal covariance function, either directly or through the construction of processes. This task is difficult as these functions should yield positive definite covariance matrices. In recent years, we have seen a flourishing of methods and theories on constructing spatio-temporal covariance functions satisfying the positive definiteness requirement. The current state-of-the-art when modeling environmental processes are those that embed the associated physical laws of the system. The class of Lagrangian spatio-temporal covariance functions fulfills this requirement. Moreover, this class possesses the allure that they turn already established purely spatial covariance functions into spatio-temporal covariance functions by a direct application of the concept of Lagrangian reference frame. In this dissertation, several developments are proposed and new features are provided to this special class.