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Langevin Picture of Subdiffusion with Infinitely Divisible Waiting Times

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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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Authors and Affiliations

  1. Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, 50-370, Wroclaw, Poland

    Marcin Magdziarz

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  1. Marcin Magdziarz
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Correspondence to Marcin Magdziarz.

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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

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