2009/01/08 by T. Srokowski, Tomasz Srokowski · 12 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Anomalous diffusion #Diffusion #Diffusion and Search Dynamics #Exponential distribution #Exponential function #Fractional Differential Equations Solutions #Gaussian #Gaussian process #Jumping #Lévy flight #Mathematical analysis #Mathematics #Monte Carlo method #Physics #Quantum mechanics #Random walk #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Truncation (statistics) #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physa.2008.12.059
published in Physica A Statistical Mechanics and its Applications 388(7), 1057-1066 (Elsevier BV) · 19 pages, 5 figures
openalex publication_date 2009/01/08 · arxiv created 2009/06/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Lévy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable diffusion coefficient, is solved in the diffusion limit. That solution resolves itself to the stretched Gaussian when the order parameter μ→2. The truncation of the Lévy flights, in the exponential and power-law form, is introduced and the corresponding random walk process is simulated by the Monte Carlo method. The stretched Gaussian tails are found in both cases. The time which is needed to reach the limiting distribution strongly depends on the jumping rate parameter. When the cutoff function falls slowly, the tail of the distribution appears to be algebraic.