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Tempered fractional Brownian motion on finite intervals

Author

Listed:
  • Thomas Vojta

    (Missouri University of Science and Technology)

  • Zachary Miller

    (Missouri University of Science and Technology)

  • Samuel Halladay

    (Missouri University of Science and Technology
    Yale University)

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. Graphic abstract

Suggested Citation

  • Thomas Vojta & Zachary Miller & Samuel Halladay, 2021. "Tempered fractional Brownian motion on finite intervals," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(10), pages 1-11, October.
    • Handle: RePEc:spr:eurphb:v:94:y:2021:i:10:d:10.1140_epjb_s10051-021-00208-6
    DOI: 10.1140/epjb/s10051-021-00208-6
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