  Fractional Brownian motion is a Gaussian stochastic process with stationary,
long-time correlated increments and is frequently used to model anomalous
diffusion processes. We study numerically fractional Brownian motion confined
to a finite interval with reflecting boundary conditions. The probability
density function of this reflected fractional Brownian motion at long times
converges to a stationary distribution showing distinct deviations from the
fully flat distribution of amplitude $1/L$ in an interval of length $L$ found
for reflected normal Brownian motion. While for superdiffusion, corresponding
to a mean squared displacement $\langle X^2(t)\rangle\simeq t^{\alpha}$ with
$1<\alpha<2$, the probability density function is lowered in the centre of the
interval and rises towards the boundaries, for subdiffusion ($0<\alpha<1$) this
behaviour is reversed and the particle density is depleted close to the
boundaries. The mean squared displacement in these cases at long times
converges to a stationary value, which is, remarkably, monotonically increasing
with the anomalous diffusion exponent $\alpha$. Our a priori surprising results
may have interesting consequences for the application of fractional Brownian
motion for processes such as molecule or tracer diffusion in the confined of
living biological cells or organelles, or other viscoelastic environments such
as dense liquids in microfluidic chambers.
