2011/10/31 by S. I. Denisov, S. B. Yuste, Yu. S. Bystrik +4 · 1 citation
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Statistical Distribution Estimation and Applications #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.84.061143
published as Phys. Rev. E 84, 061143 (2011) · 16 pages, 1 figure
arxiv created 2011/12/27 · openalex publication_date 2011/12/27 · arxiv updated 2011/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time. We show that the probability density of the scaled walker position converges in the long-time limit to a nondegenerate one only if the scaling function behaves in a certain way. This function as well as the limiting probability density are determined in explicit form. Also, we express the limiting probability density which has heavy tails in terms of the Fox H function and find its behavior for small and large distances.