Langevin description of superdiffusive Lévy processes

Eule S, Zaburdaev V, Friedrich R, Geisel T (2012)

Publication Type: Journal article

Publication year: 2012

Journal

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics American Physical Society (APS)

Book Volume: 86

Article Number: 041134

Journal Issue: 4

DOI: 10.1103/PhysRevE.86.041134

Abstract

The description of diffusion processes is possible in different frameworks such as random walks or Fokker-Planck or Langevin equations. Whereas for classical diffusion the equivalence of these methods is well established, in the case of anomalous diffusion it often remains an open problem. In this paper we aim to bring three approaches describing anomalous superdiffusive behavior to a common footing. While each method clearly has its advantages it is crucial to understand how those methods relate and complement each other. In particular, by using the method of subordination, we show how the Langevin equation can describe anomalous diffusion exhibited by Lévy-walk-type models and further show the equivalence of the random walk models and the generalized Kramers-Fokker-Planck equation. As a result a synergetic and complementary description of anomalous diffusion is obtained which provides a much more flexible tool for applications in real-world systems. © 2012 American Physical Society.

Authors with CRIS profile

Vasily Zaburdaev

Involved external institutions

Max-Planck-Institut für Dynamik und Selbstorganisation / Max Planck Institute for Dynamics and Self-Organization DE Germany (DE) Harvard University US United States (USA) (US) Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE)

How to cite

APA:

Eule, S., Zaburdaev, V., Friedrich, R., & Geisel, T. (2012). Langevin description of superdiffusive Lévy processes. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 86(4). https://doi.org/10.1103/PhysRevE.86.041134

MLA:

Eule, S., et al. "Langevin description of superdiffusive Lévy processes." Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 86.4 (2012).

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