2017/03/22 by Mohsen Ghasemi Nezhadhaghighi, M. Ghasemi Nezhadhaghighi
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Anomalous diffusion #Complex Systems and Time Series Analysis #Diffusion process #Entropy (arrow of time) #Exponent #Mathematics #Physics #Power law #Probability density function #Probability distribution #Quantum mechanics #Scaling #Spectral density #Statistical Mechanics and Entropy #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.96.022113
published as Phys. Rev. E 96, 022113 (2017) · 8 pages, 5 figures
arxiv created 2017/03/22 · openalex publication_date 2017/08/07 · arxiv updated 2017/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.