Anthony Réveillac (INSA Toulouse)
Gregor Pasemann (HU)
We consider the problem of estimating the diffusivity of a stochastic heat equation (or more generally, the parametrized drift of an abstract linear stochastic parabolic evolution equation) from spectral or local measurements perturbed by small observation noise. Using a kernel smoothing approach, we construct a modified maximum likelihood estimator and study its asymptotic properties. In particular, we find an optimal tradeoff between exploiting small-scale spatial information and averaging out the observation noise.
This talk is based on work in progress with Markus Reiß.