TY  - JOUR
A1  - Toenjes, Ralf
A1  - Sokolov, Igor M.
A1  - Postnikov, Eugene B.
T1  - Spectral properties of the fractional Fokker-Planck operator for the Levy flight in a harmonic potential
JF  - The European physical journal
N2  - 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.
Y1  - 2014
U6  - https://doi.org/10.1140/epjb/e2014-50558-5
SN  - 1434-6028
SN  - 1434-6036
VL  - 87
IS  - 12
PB  - Springer
CY  - New York
ER  -