2003/10/31 by S. B. Yuste, Santos B. Yuste, L. Acedo
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Fractional Differential Equations Solutions #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.69.031104
published as Phys. Rev. E 69, 031104 (2004) · 4 pages, 6 figures. Accepted for publication Phys. Rev. E (Replaced for the latest version, in press.) Section II rewritten
arxiv created 2004/02/19 · openalex publication_date 2004/03/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the average shape of fluctuations for subdiffusive processes, i.e., processes with uncorrelated increments but where the waiting time distribution has a broad power-law tail. This shape is obtained analytically by means of a fractional diffusion approach. We find that, in contrast with processes where the waiting time between increments has finite variance, the fluctuation shape is no longer a semicircle: it tends to adopt a tablelike form as the subdiffusive character of the process increases. The theoretical predictions are compared with numerical simulation results.