Hurst index estimation for SPDEs - seminar with Pavel Kriz

Fractional Brownian motion (fBm) has been considered as a stochastic process generating autocorrelated (colored) Gaussian noise in various stochastic models for many decades. The so called Hurst index determines regularity, self-similarity and covariance structure of this process. Although there is a vast literature on Hurst index estimation for scalar fBm, not much has been done on its estimation for SPDEs driven by fBm so far (except for few papers with very special observational schemes and limited use). We have recently initiated a research on this topic (Hurst index estimation for semilinear SPDEs driven by cylindrical fBm) and I will discuss some preliminary results and ideas with illustration both on synthetic and real data during the talk. The presented work is still in progress and is conducted in cooperation with Gregor Pasemann and Markus Reiß.