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Fractional Brownian motion with a reflecting wall

Alexander H. O. Wada and Thomas Vojta
Phys. Rev. E 97, 020102(R) – Published 13 February 2018

Abstract

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior x2tα, the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case α>1, the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion α<1, in contrast, the probability density is depleted close to the barrier. We discuss implications of these findings, in particular, for applications that are dominated by rare events.

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  • Received 22 November 2017
  • Revised 28 December 2017

DOI:https://doi.org/10.1103/PhysRevE.97.020102

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Alexander H. O. Wada1,2 and Thomas Vojta1,3

  • 1Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
  • 2Instituto de Física, Universidade de São Paulo, Rua do Matão, 1371, 05508-090 São Paulo, São Paulo, Brazil
  • 3Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA

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Issue

Vol. 97, Iss. 2 — February 2018

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