  Finite dimensional solutions to a class of stochastic partial differential
equations are obtained extending the differential constraints method for
deterministic PDE to the stochastic framework. A geometrical reformulation of
the stochastic problem using the concept of infinite jet bundles is provided
and a practical algorithm for explicitly computing these finite dimensional
solutions is developed. This method, covering the majority of the current
literature, is applied to a set of new SPDEs admitting finite dimensional
solutions taken from Heath-Jarrow-Morton framework, stochastic hydrodynamics
and filtering theory.
