Anomalous diffusion and the first passage time problem

2000/07/01 by Govindan Rangarajan, Mingzhou Ding · 3 citations
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech #math.PR #physics.chem-ph

paper · pdf · doi:10.1103/physreve.62.120

published as Phys. Rev. E62 (2000) 120-133 · 25 pages, 4 figures

openalex publication_date 2000/07/01 · arxiv created 2001/05/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the distribution of the first passage time (FPT) in Levy type anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in terms of Fox or H functions when the diffusion has zero drift. (2) For the nonzero drift case we obtain an analytical expression for the Laplace transform of the FPT distribution. (3) We express the FPT distribution in terms of a power series for the case of two absorbing barriers. The known results for ordinary diffusion (Brownian motion) are obtained as special cases of our more general results.

Citations

• Fractional diffusion and Lévy stable processes
• Diffusion in disordered media

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