  This work is concerned with the dynamics of a slow-fast stochastic
evolutionary system quantified with a scale parameter. An invariant foliation
decomposes the state space into geometric regions of different dynamical
regimes, and thus helps understand dynamics. A slow invariant foliation is
established for this system. It is shown that the slow foliation converges to a
critical foliation (i.e., the scale parameter is zero) in probability
distribution, as the scale parameter tends to zero. The approximation of slow
foliation is also constructed with error estimate in distribution. Furthermore,
the geometric structure of the slow foliation is investigated: every fiber of
the slow foliation parallels each other, with the slow manifold as a special
fiber. In fact, when an arbitrarily chosen point of a fiber falls in the slow
manifold, the fiber must be the slow manifold itself.
