B1749
Title: Anomalous diffusion processes with random parameters
Authors: Agnieszka Wylomanska - Wroclaw University of Science and Technology (Poland) [presenting]
Abstract: The anomalous diffusion processes are useful for the description of various real phenomena including financial markets, condition monitoring and biological experiments. However, recent experiments show that the classical models seem to be insufficient to reflect the nature of the analyzed phenomena. Thus, in the recent literature one can find various modifications of the anomalous diffusive processes to capture specific behavior of real data. One of the modifications is the introduction of random parameters responsible for the anomalous diffusive behaviour in the classical models. The idea of the new concept of anomalous diffusive models is presented. The main attention is paid to the fractional Brownian motion (FBM) and multifractional FBM, where the Hurst exponent is replaced by the appropriate random variable and stochastic process, respectively. The main probabilistic properties of modified classical models are presented and the procedures for real data analysis are discussed. Finally, real data examples are presented.
