Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion

Abstract EN

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 α-stable subordinator.

We compute the mean square displacement of the proposed process and show that the process exhibits subdiffusion when 0<α<1/3, normal diffusion when α=1/3, and superdiffusion when 1/3<α<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.