How to Distinguish Fractional Brownian Motion with Random and Constant Hurst Exponents

Explore the intricacies of fractional Brownian motion (FBM) in this 27-minute conference talk delivered by Agnes Wylomanska at the Workshop on "Transport Properties in Soft Matter Systems" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into the challenges of distinguishing between FBM models with constant and random Hurst exponents. Examine the probabilistic properties of statistics represented by quadratic forms and their application in Gaussian processes. Learn about the sample autocovariance function and empirical anomaly measure as key statistics for model differentiation. Discover a novel testing procedure designed to differentiate between the two FBM models. Review analytical and simulation results, considering two-point and beta distributions as examples of random Hurst exponent distributions. Witness the practical application of this methodology through analysis of real-world datasets from financial markets and single-particle tracking experiments in biological gels.