  Fractional Brownian motion, a stochastic process with long-time correlations
between its increments, is a prototypical model for anomalous diffusion. We
analyze fractional Brownian motion in the presence of a reflecting wall by
means of Monte Carlo simulations. While the mean-square displacement of the
particle shows the expected anomalous diffusion behavior $\langle x^2 \rangle
\sim t^\alpha$, the interplay between the geometric confinement and the
long-time memory leads to a highly non-Gaussian probability density function
with a power-law singularity at the barrier. In the superdiffusive case,
$\alpha> 1$, the particles accumulate at the barrier leading to a divergence of
the probability density. For subdiffusion, $\alpha < 1$, in contrast, the
probability density is depleted close to the barrier. We discuss implications
of these findings, in particular for applications that are dominated by rare
events.
