  We study the effects of noise on a recently discovered form of intermittency,
referred to as in-out intermittency. This type of intermittency, which reduces
to on-off in systems with a skew product structure, has been found in the
dynamics of maps, ODE and PDE simulations that have symmetries. It shows itself
in the form of trajectories that spend a long time near a symmetric state
interspersed with short bursts away from symmetry. In contrast to on-off
intermittency, there are clearly distinct mechanisms of approach towards and
away from the symmetric state, and this needs to be taken into account in order
to properly model the long time statistics. We do this by using a
diffusion-type equation with delay integral boundary condition. This model is
validated by considering the statistics of a two-dimensional map with and
without the addition of noise.
