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arXiv · 1306.1667

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

Jae-Hyung Jeon·Aleksei V. Chechkin·Ralf Metzler
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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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Jae-Hyung Jeon, Aleksei V. Chechkin, Ralf Metzler. 2013-06-13. First passage behaviour of multi-dimensional fractional Brownian motion and application to reaction phenomena. https://arxiv.org/abs/1306.1667

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