  Noise-induced statistical periodicity in a class of one-dimensional maps is
studied. We show the existence of statistical periodicity in a modified
Lasota-Mackey map and describe the phenomenon in terms of almost cyclic sets. A
transition from a stable state to a periodic state of the density depending on
the noise level is observed in numerical investigations based on trajectory
averages and by means of a transfer operator approach. We conclude that the
statistical periodicity is the origin of the almost periodicity in
noise-induced order.
