Langevin Picture of Subdiffusion with Infinitely Divisible Waiting Times

Abstract

In this paper we study a Langevin approach to modeling of subdiffusion in the presence of time-dependent external forces. We construct a subordinated Langevin process, whose probability density function solves the subdiffusive fractional Fokker-Planck equation. We generalize the results known for the Levy-stable waiting times to the case of infinitely divisible waiting-time distributions. Our approach provides a complete mathematical description of subdiffusion with time-dependent forces. Moreover, it allows to study the trajectories of the constructed process both analytically and numerically via Monte-Carlo methodology.