Spectral properties of the fractional Fokker-Planck operator for the Levy flight in a harmonic potential
- 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.
| Author details: | Ralf ToenjesORCiD, Igor M. SokolovORCiDGND, Eugene B. Postnikov |
|---|---|
| DOI: | https://doi.org/10.1140/epjb/e2014-50558-5 |
| ISSN: | 1434-6028 |
| ISSN: | 1434-6036 |
| Title of parent work (English): | The European physical journal |
| Publisher: | Springer |
| Place of publishing: | New York |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2014 |
| Publication year: | 2014 |
| Release date: | 2017/03/26 |
| Volume: | 87 |
| Issue: | 12 |
| Number of pages: | 11 |
| Funding institution: | RFBR [14-02-91337 NNIO_a] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| Peer review: | Referiert |
