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 Lévy-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.
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Magdziarz, M. Langevin Picture of Subdiffusion with Infinitely Divisible Waiting Times. J Stat Phys 135, 763–772 (2009). https://doi.org/10.1007/s10955-009-9751-z
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DOI: https://doi.org/10.1007/s10955-009-9751-z