Tempered Fractional Brownian Motion on Finite Intervals
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.
T. Vojta et al., "Tempered Fractional Brownian Motion on Finite Intervals," European Physical Journal B, vol. 94, no. 10, article no. 208, EDP Sciences, Oct 2021.
The definitive version is available at https://doi.org/10.1140/epjb/s10051-021-00208-6
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14 Oct 2021
This work was supported in part by a Cottrell SEED award from Research Corporation and by the National Science Foundation under Grant Nos. DMR-1828489 and OAC-1919789.