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

Ralf Toenjes (), Igor M. Sokolov and Eugene B. Postnikov

The European Physical Journal B: Condensed Matter and Complex Systems, 2014, vol. 87, issue 12, 1-11

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

Keywords: Statistical and Nonlinear Physics (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1140/epjb/e2014-50558-5

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