A0491
Title: Distinguishing anomalous diffusion: A statistical approach to parameter characterization
Authors: Agnieszka Wylomanska - Wroclaw University of Science and Technology (Poland) [presenting]
Katarzyna Maraj-Zygmat - Wroclaw University of Science and Technology (Poland)
Aleksandra Grzesiek - Wroclaw Univeristy of Science and Technology (Poland)
Diego Krapf - Colorado State University (United States)
Abstract: Anomalous diffusion describes processes where a particle's mean squared displacement scales non-linearly with time. This behavior, common in complex systems (like biological cells), goes beyond standard diffusion. Traditional models like fractional Brownian motion (FBM) and scaled Brownian motion (SBM) assume a constant anomalous diffusion exponent, which limits their ability to capture dynamics with varying anomalous parameters. To overcome this, FBM with random exponents (FBMRE) and SBM with random exponents (SBMRE) were developed. This research introduces a universal statistical testing framework to differentiate between anomalous diffusion models having constant versus random anomalous exponents. It uses time-averaged statistics and their ratios. This methodology broadly applies to constant vs. random anomalous diffusion scenarios, with its effectiveness depending on chosen statistics, time lags, and process properties. This is demonstrated through simulations (using a two-point exponent distribution) and real-world data analysis.
