Randolf Altmeyer: Nonparametric estimation problems for linear SPDEs

Speaker
Randolf Altmeyer, Imperial College London

Abstract
We consider a stochastic heat equation, where both the diffusivity with respect to the linear operator and the noise level with respect to a Wiener process are variable (space dependent). In recent years, several estimators, usually based on power variations, were developed for constant diffusivity and constant noise level, when the solution of the SPDE is observed over a finite time interval and on a spatial grid. In this work, we develop a general nonparametric estimation framework that applies to large class of linear SPDEs with colored noise, and which covers as particular cases methods based on power variations for spatially discrete observations and local measurements.