Non-Gaussian Behavior of Reflected Fractional Brownian Motion
A possible mechanism leading to anomalous diffusion is the presence of long-range correlations in time between the displacements of the particles. Fractional Brownian motion, a non-Markovian self-similar Gaussian process with stationary increments, is a prototypical model for this situation. Here, we extend the previous results found for unbiased reflected fractional Brownian motion (Wada et al 2018 Phys. Rev. E 97 020102) to the biased case by means of Monte Carlo simulations and scaling arguments. We demonstrate that the interplay between the reflecting wall and the correlations leads to highly non-Gaussian probability densities of the particle position x close to the reflecting wall. Specifically, the probability density P(x) develops a power-law singularity P ~ xk with k < 0 if the correlations are positive (persistent) andk > 0 if the correlations are negative (antipersistent). We also analyze the behavior of the large-x tail of the stationary probability density reached for bias towards the wall, the average displacements of the walker, and the first-passage time, i.e. the time it takes for the walker reach position x for the first time.
A. H. Wada et al., "Non-Gaussian Behavior of Reflected Fractional Brownian Motion," Journal of Statistical Mechanics: Theory and Experiment, vol. 2019, no. 3, Institute of Physics - IOP Publishing, Mar 2019.
The definitive version is available at https://doi.org/10.1088/1742-5468/ab02f1
Center for High Performance Computing Research
Keywords and Phrases
Brownian motion; classical phase transitions; difiusion
International Standard Serial Number (ISSN)
Article - Journal
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01 Mar 2019