Modeling anomalous diffusion by a subordinated integrated Brownian motion
Summary: We consider a particular type of continuous time random walk where the jump lengths between subsequent waiting times are correlated. In a continuum limit, the process can be defined by an integrated Brownian motion subordinated by an inverse \(\alpha\)-stable subordinator. We compute the mean square displacement of the proposed process and show that the process exhibits subdiffusion when \(0 < \alpha < 1 / 3\), normal diffusion when \(\alpha = 1 / 3\), and superdiffusion when \(1 / 3 < \alpha < 1\). The time-averaged mean square displacement is also employed to show weak ergodicity breaking occurring in the proposed process. An extension to the fractional case is also considered.
scientific article; zbMATH DE number 6962664
scientific article