@article{ToenjesSokolovPostnikov2014,
  author    = {Toenjes, Ralf and Sokolov, Igor M. and Postnikov, Eugene B.},
  title     = {Spectral properties of the fractional Fokker-Planck operator for the Levy flight in a harmonic potential},
  series = {The European physical journal},
  volume    = {87},
  journal   = {The European physical journal},
  number    = {12},
  publisher = {Springer},
  address   = {New York},
  issn      = {1434-6028},
  doi       = {10.1140/epjb/e2014-50558-5},
  pages     = {11},
  year      = {2014},
  abstract  = {We present a detailed analysis of the eigenfunctions of the Fokker-Planck operator for the LevyOrnstein- 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 Levy-Ornstein-Uhlenbeck process and their correlation functions.},
  language  = {en}
}