Nexira (France)

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

International audience

This paper describes a methodology to build a combined conducted and radiated emission model for integrated circuits. The development of emission models of a FPGA extracted from two different approaches is presented and discussed. The first approach allows to build a predictable model from FPGA implementation and some passive measurement on FPGA device. The second approach allows to build a model from only the near field measurement. In conclusion, the accuracy of both models as well as the advantages and disadvantages are discussed.