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 have investigated tempered fractional Brownian motion confined to a finite interval by reflecting walls. Specifically, we have explored 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 have found 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.