  Supernova remnants are expected to contain braided (or stochastic) magnetic
fields, which are in some regions directed mainly perpendicular to the shock
normal. For particle acceleration due to repeated shock crossings, the
transport in the direction of the shock normal is crucial. The mean squared
deviation along the shock normal is then proportional to the square root of the
time. This kind of anomalous transport is called sub-diffusion. We use a
Monte-Carlo method to examine this non-Markovian transport and the
acceleration. As a result of this simulation we are able to examine the
propagator, density and pitch-angle distribution of accelerated particles, and
especially the spectral properties. These are in broad agreement with analytic
predictions for both the sub-diffusive and the diffusive regimes, but the
steepening of the spectrum predicted when changing from diffusive to
sub-diffusive transport is found to be even more pronounced than predicted.
