Pavel Kříž: Estimating the Self-Similarity Index for Parabolic SPDEs

Speaker
Pavel Kříž, Charles University

Abstract
In this talk, we present a method for estimating the Hurst (self-similarity) index of the driving noise in the stochastic heat equation. The core idea is to extend the widely-used quadratic variation approach, typically applied to scalar processes, to spatio-temporal data. To achieve this, temporal rescaling is replaced by a (parabolic) spatio-temporal rescaling, ensuring that the estimation procedure is consistent in both time (with increasing temporal resolution) and space (with increasing spatial resolution), while maintaining natural convergence rates. This spatio-temporal approach will be examined in the context of two common observation settings: spectral and local. The talk is based on the joint work with Gregor Pasemann and Markus Reiß.