2010/03/31 by S. I. Denisov, Hölger Kantz, H. Kantz +2 · 35 citations
Mathematics · Physics and Astronomy · #Computer science #Connection (principal bundle) #Differential equation #Distribution (mathematics) #Fokker–Planck equation #Fractional Differential Equations Solutions #Geometry #Langevin dynamics #Langevin equation #Mathematical analysis #Mathematics #Noise (video) #Physics #Quantum mechanics #Statistical Mechanics and Entropy #Statistical physics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1751-8113/43/28/285004
published in Journal of Physics A Mathematical and Theoretical 43(28), 285004 (Institute of Physics) · 12 pages, 3 figures
arxiv created 2010/06/14 · openalex publication_date 2010/06/14 · arxiv updated 2010/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We extend the Langevin approach to a class of driving noises whose generating processes have independent increments with super-heavy-tailed distributions. The time-dependent generalized Fokker-Planck equation that corresponds to the first-order Langevin equation driven by such a noise is derived and solved exactly. This noise generates two probabilistic states of the system, survived and absorbed, that are equivalent to those for a classical particle in an absorbing medium. The connection between the rate of absorption and the super-heavy-tailed distribution of the increments is established analytically. A numerical scheme for the simulation of the Langevin equation with super-heavy-tailed noise is developed and used to verify our theoretical results.