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arXiv · 2107.10774

Tempered fractional Brownian motion on finite intervals

Thomas Vojta·Zachary Miller·Samuel Halladay
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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.

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Thomas Vojta, Zachary Miller, Samuel Halladay. 2021-07-22. Tempered fractional Brownian motion on finite intervals. https://doi.org/10.1140/epjb/s10051-021-00208-6

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