@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