Steady-state Lévy flights in a confined domain

2008/04/30 by S. I. Denisov, Werner Horsthemke, Peter Hänggi · 4 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #Fractional Differential Equations Solutions #cond-mat.soft #cond-mat.stat-mech #stochastic dynamics and bifurcation

paper · pdf · doi:10.1103/physreve.77.061112

published as Phys. Rev. E 77, 061112 (2008) · 10 pages, 1 figure

openalex publication_date 2008/06/10 · arxiv created 2008/06/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 boundaries of the well. The origin of the preferred concentration of flying objects near the boundaries in nonequilibrium systems is clarified.

Citations

• Stochastic Processes in Physics and Chemistry

Cited by

• Langevin equation with super-heavy-tailed noise
• Lévy Flights in Steep Potential Wells: Langevin Modeling Versus Direct Response to Energy Landscapes
• Lévy on-off intermittency
• Multimodal stationary states in symmetric single-well potentials driven by Cauchy noise

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