2008/07/31 by M. A. Rajabpour · 1 citation
Mathematics · Physics and Astronomy · #Brownian excursion #Brownian motion #Cauchy distribution #Differential equation #Diffusion process #Distribution (mathematics) #Fokker–Planck equation #Fractal #Fractional Brownian motion #Fractional Differential Equations Solutions #Geometric Brownian motion #Mathematical analysis #Mathematical physics #Mathematics #Physics #Propagator #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/41/42/425001
published in Journal of Physics A Mathematical and Theoretical 41(42), 425001 (Institute of Physics) · 8 pages, published version, minor changes
openalex publication_date 2008/09/29 · arxiv created 2009/02/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We find the exact winding number distribution of Riemann–Liouville fractional Brownian motion for large times in two dimensions using the propagator of a free particle. The distribution is similar to the Brownian-motion case and is of Cauchy type. In addition we find the winding number distribution of the fractal-time process, i.e. the time-fractional Fokker–Planck equation, in the presence of a finite-size winding center.