Lauri Viitasaari (Aalto University) – Some statistical aspects related to SPDEs

In this talk we discuss several aspects statistical aspects related to SPDEs. In particular, we provide quantitative central limit theorem results for spatial averages of solutions under rather general conditions on both the differential operator and on the noise term. On top of that, we consider non-parametric estimation of the unknown diffusion coefficient. We define an estimator that is shown to be consistent. We also provide the rate of convergence in the $L^p$ norm.