Steady-state Lévy flights in a confined domain.

@article{Denisov2008SteadystateLF,
  title={Steady-state L{\'e}vy flights in a confined domain.},
  author={Sergey Denisov and Werner Horsthemke and Peter H{\"a}nggi},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2008},
  volume={77 6 Pt 1},
  pages={061112}
}
We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric Lévy flights in an infinitely deep potential well. The fractional Fokker-Planck equation for Lévy flights is derived and solved analytically in the steady state. It is shown that Lévy flights are distributed according to the beta distribution, whose probability density becomes singular at the… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 24 references

The Langevin Equation

W T Coffey, Yu P Kalmykov, J T Waldron
The Langevin Equation • 2004

͓2͔ Lévy Flights and Related Topics in Physics

͓2͔ Lévy Flights and Related Topics in Physics • 1995

Fractional Integrals and Derivatives: Theory and Applications ͑Gordon and Breach

S G Samko, A A Kilbas, O I Marichev
Fractional Integrals and Derivatives: Theory and Applications ͑Gordon and Breach • 1993

Stochastic Processes in Physics and Chemistry ͑North-Holland

N G Van Kampen
Stochastic Processes in Physics and Chemistry ͑North-Holland • 1992

One-Dimensional Stable Distributions ͑American Mathematical Society

V M Zolotarev
One-Dimensional Stable Distributions ͑American Mathematical Society • 1986

Noise-Induced Transitions ͑Springer

W Horsthemke, R Lefever
Noise-Induced Transitions ͑Springer • 1984

Limit Distributions for Sums of Independent Random Variables ͑Addison-Wesley

B V Gnedenko, A N Kolmogorov
Limit Distributions for Sums of Independent Random Variables ͑Addison-Wesley • 1954

Higher Transcendental Functions ͑McGraw-Hill

H Bateman, A Erdélyi
Higher Transcendental Functions ͑McGraw-Hill • 1953

Nature

A M Edwards
Nature • 1044

Acad. Sci

P Langevin
Acad. Sci

Similar Papers

Loading similar papers…