Mathias Trabs
Title: Non-parameteric estimation for linear SPDEs on arbitrary bounded domains based on discrete observations
Abstract
Most statistical methods for stochastic partial differential equations (SPDEs) based on discrete observations are limited to one space dimension or to quite restrictive settings. In order to study SPDEs on a bounded domain driven by a stochastic noise process which is white in time and possibly colored in space, we aim for bridging the gap between two popular observations schemes studied for statistics for SPDEs, namely, discrete observations and local measurements. To this end, we have to extend the local measurements approach to kernels of distribution type. This link allows us to construct a non-parametric estimator for the diffusivity based on discrete high-frequency observations.
The talk is based on joint work with Randolf Altmeyer and Florian Hildebrandt.