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Spectral properties of the fractional Fokker-Planck operator for the Lévy flight in a harmonic potential

Author

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  • Ralf Toenjes
  • Igor M. Sokolov
  • Eugene B. Postnikov

Abstract

We present a detailed analysis of the eigenfunctions of the Fokker-Planck operator for the Lévy-Ornstein-Uhlenbeck process, their asymptotic behavior and recurrence relations, explicit expressions in coordinate space for the special cases of the Ornstein-Uhlenbeck process with Gaussian and with Cauchy white noise and for the transformation kernel, which maps the fractional Fokker-Planck operator of the Cauchy-Ornstein-Uhlenbeck process to the non-fractional Fokker-Planck operator of the usual Gaussian Ornstein-Uhlenbeck process. We also describe how non-spectral relaxation can be observed in bounded random variables of the Lévy-Ornstein-Uhlenbeck process and their correlation functions. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Ralf Toenjes & Igor M. Sokolov & Eugene B. Postnikov, 2014. "Spectral properties of the fractional Fokker-Planck operator for the Lévy flight in a harmonic potential," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(12), pages 1-11, December.
    • Handle: RePEc:spr:eurphb:v:87:y:2014:i:12:p:1-11:10.1140/epjb/e2014-50558-5
    DOI: 10.1140/epjb/e2014-50558-5
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    Statistical and Nonlinear Physics;

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