Invariant manifolds for weak solutions to stochastic equations

Viability and invariance problems related to a stochastic equation in a Hil bert space H are studied. Finite dimensional invariant C-2 submanifolds of H are characterized. We derive Nagumo type conditions and prove a regularit y result: any weak solution, which is viable in a finite dimensional C-2 su bmanifold, is a strong solution. These results are related to finding finite dimensional realizations for st ochastic equations. There has recently been increased interest in connectio n with a model for the stochastic evolution of forward rate curves.