Eur. Phys. J. B (2021) 94: 208
https://doi.org/10.1140/epjb/s10051-021-00208-6

Regular Article - Statistical and Nonlinear Physics

Tempered fractional Brownian motion on finite intervals

¹ Department of Physics, Missouri University of Science and Technology, Rolla, 65409, MO, USA
² Department of Applied Physics, Yale University, New Haven, 06520, CT, USA

^a vojtat@mst.edu

Received: 30 July 2021
Accepted: 14 September 2021
Published online: 14 October 2021

Abstract

Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic correlation time the power-law correlations between the increments of fractional Brownian motion. Here, we investigate such tempered fractional Brownian motion confined to a finite interval by reflecting walls. Specifically, we explore how the tempering of the long-time correlations affects the strong accumulation and depletion of particles near reflecting boundaries recently discovered for untempered fractional Brownian motion. We find that exponential tempering introduces a characteristic size for the accumulation and depletion zones but does not affect the functional form of the probability density close to the wall. In contrast, power-law tempering leads to more complex behavior that differs between the superdiffusive and subdiffusive cases.