First passage behaviour of multi-dimensional fractional Brownian motion and application to reaction phenomena

2013/06/07 by Jae‐Hyung Jeon, Aleksei V. Chechkin, Jeon, Jae-Hyung +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Physical sciences #Fractional Differential Equations Solutions #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1306.1667

openalex publication_date 2013/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Fractional Brownian motion is a generalised Gaussian diffusive process that is found to describe numerous stochastic phenomena in physics and biology. Here we introduce a multi-dimensional fractional Brownian motion (FBM) defined as a superposition of conventional FBM for each coordinate in analogy to multi-dimensional Brownian motion, and study its first passage properties. Starting from the well-established first passage time statistics of one-dimensional FBM and the associated approximation schemes, we explore the first passage time behaviour of multi-dimensional FBM and compare these results with simulations. The asymptotic kinetic behaviour of diffusion-limited reactions of reactant particles performing FBM in a one- and multi-dimensional space is studied based on the corresponding first passage time statistics.

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