Nonlinear dynamics of continuous-time random walks in inhomogeneous medium.

Continuous-time random walks (CTRWs) are an elementary model for particle motion subject to randomized waiting times. In this paper, we consider the case where the distribution of waiting times depends on the location of the particle. In particular, we analyze the case where the medium exhibits a bounded trapping region in which the particle is subject to CTRW with power-law waiting times and regular diffusion elsewhere.

Analytic model for transient anomalous diffusion with highly persistent correlations.

In recent decades, many stochastic processes have been proposed as models for real world time series data with anomalous spreading, highly persistent correlations, and transient distributional characteristics. We introduce the higher order fractional tempered stable motion as the stochastic integral of the tempered stable motion with respect to a generalized higher order moving average kernel, which provides an analytic model for stochastic processes possessing these characteristics. This stochastic process provides a mathematical model for anomalous diffusion with a transient distribution resembling higher order fractional stable motion on short timescales and higher order fractional Brownian motion in the long run.