Lukas Trottner: Change point estimation for a stochastic heat equation

Speaker
Lukas Trottner, Univ. of Birmingham

Abstract
We study a change point model in an infinite-dimensional setting, where we consider a parabolic SPDE, which has a piecewise constant diffusivity coefficient and is driven by space-time white noise. Assuming that our data are given by observing the solution to the SPDE locally in space at resolution $\delta$ and continuously in time, we introduce a novel simultaneous M-estimator for the diffusivity parameters and the change point, which converges at optimal rates for non-vanishing signal. Under a faint signal condition given by a vanishing jump height in the diffusivity, we derive a limit theorem for the change point estimator, where the limiting distribution is the law of the minimiser of a two-sided Brownian motion with drift. Finally, we demonstrate how our methodology can be extended to multivariate spatial dimensions, where we face the nonparametric task of identifying a change domain from local measurements. This talk is based on joint works with Markus Reiß, Claudia Strauch and Anton Tiepner.