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We study the dynamics of waves, oscillations, and other spatio-temporalpatterns in stochastic evolution systems, including SPDE and stochasticintegral equations. Representing a given pattern as a smooth, stable invariantmanifold of the deterministic dynamics, we reduce the stochastic dynamics to afinite dimensional SDE on this manifold using the isochronal phase. Theisochronal phase is defined by mapping a neighbourbhood of the manifold ontothe manifold itself, analogous to the isochronal phase defined forfinite-dimensional oscillators by A.T.~Winfree and J.~Guckenheimer. We thendetermine a probability measure that indicates the average position of thestochastic perturbation of the pattern/wave as it wanders over the manifold. Itis proved that this probability measure is accurate on time-scales greater than$O(\sigma^{-2})$, but less than $O(\exp(C\sigma^{-2}))$, where $\sigma\ll1$ isthe amplitude of the stochastic perturbation. Moreover, using this measure, wedetermine the expected velocity of the difference between the deterministic andstochastic motion on the manifold.

The Isochronal Phase of Stochastic PDE and Integral Equations: Metastability and Other Properties