  We study the dynamics of waves, oscillations, and other spatio-temporal
patterns in stochastic evolution systems, including SPDE and stochastic
integral equations. Representing a given pattern as a smooth, stable invariant
manifold of the deterministic dynamics, we reduce the stochastic dynamics to a
finite dimensional SDE on this manifold using the isochronal phase. The
isochronal phase is defined by mapping a neighbourbhood of the manifold onto
the manifold itself, analogous to the isochronal phase defined for
finite-dimensional oscillators by A.T.~Winfree and J.~Guckenheimer. We then
determine a probability measure that indicates the average position of the
stochastic perturbation of the pattern/wave as it wanders over the manifold. It
is proved that this probability measure is accurate on time-scales greater than
$O(\sigma^{-2})$, but less than $O(\exp(C\sigma^{-2}))$, where $\sigma\ll1$ is
the amplitude of the stochastic perturbation. Moreover, using this measure, we
determine the expected velocity of the difference between the deterministic and
stochastic motion on the manifold.
