Markus Reiß: Statistics for SPDEs – a survey I

Speaker
Markus Reiß, Humboldt University Berlin

Abstract
We discuss basic approaches for statistical methods in SPDE models. As we shall see, the observation scheme is of fundamental importance, which leads to spectral, pointwise and local estimators of coefficients in the SPDE. Further key differences arise from the order of (spatial) derivative the coefficient appears in. Turning from a parametric statistics perspective to nonparametrics where the coefficient is a function of space and/or time, this issue will lead to different rates of estimation. Finally, we shall consider additional measurement error, which we call static noise, as opposed to dynamic noise in the SPDE, and understand the contrary influence of the respective noise levels on the statistical accuracy. The presentation will have review character and aims at introucing the non-specialists to the field.