A general framework for SPDE-based stationary random fields

This paper presents theoretical advances in the application of Stochastic Partial Differential Equation (SPDE) approach geostatistics. We show a general to construct stationary models related wide class linear SPDEs, with applications spatio-temporal having non-trivial properties. Within framework Generalized Random Fields, criterion for existence and uniqueness solutions this SPDEs is proposed proven. Their covariance are then obtained through their spectral measure. present result relating solution case White Noise source term generic convolution. Then, we obtain variety SPDE-based random fields. In particular, well-known results regarding Matérn Model Markovian recovered. A new relationship between Stein model particular SPDE obtained. New from evolution arbitrary temporal derivative order obtained, which properties separability symmetry can be controlled. also concerning physically inspired models, such as heat equation, advection-diffusion some Langevin’s equations wave equation.