Title: Modelling of anomalous diffusion processes with random parameters
Authors: Agnieszka Wylomanska - Wroclaw University of Science and Technology (Poland) [presenting]
Abstract: Anomalous diffusion processes are observed in various phenomena. One of the classical anomalous diffusion model is the fractional Brownian motion (FBM), a Gaussian non-Markovian self-similar process with stationary long-correlated increments. The correlation and diffusion properties of this random motion are fully characterized by its Hurst exponent. However, recent biological experiments revealed highly complicated anomalous diffusion phenomena that can not be attributed to a class of self-similar random processes. Inspired by these observations, we study the process which preserves the properties of FBM at a single trajectory level; however, the Hurst index randomly changes from trajectory to trajectory. We provide a general mathematical framework for analytical, numerical and statistical analysis of FBM with random Hurst exponent. The explicit formulas for probability density function, mean square displacement and autocovariance function of the increments are presented for three generic distributions of the Hurst exponent, namely two-point, uniform and beta distributions. The important features of the process studied here are accelerating diffusion and persistence transition, which we demonstrate analytically and numerically.