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B1400
Title: Parameter estimation for anisotropic SPDEs from multiple local measurements Authors:  Randolf Altmeyer - Cambridge University (United Kingdom) [presenting]
Martin Wahl - Humboldt University of Berlin (Germany)
Anton Tiepner - Aarhus University (Denmark)
Abstract: The purpose is to discuss how the coefficients in a general second-order linear stochastic partial differential equation (SPDE) can be estimated. Given multiple spatially localised measurements, estimators for the diffusivity, transport and reaction coefficients are constructed. All coefficients are allowed to be anisotropic. With the spatial resolution of the measurements tending to zero and assuming a growing number of measurements, the constructed estimators achieve the optimal rate of convergence. For each coefficient, this rate depends on the order of the respective differential operator with the best rate for the diffusivity and the worst rate for the reaction terms.