  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.
