Invariant manifolds for stochastic partial differential equations in continuously embedded Hilbert spaces

Abstract

We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds for solutions of stochastic partial differential equations (SPDEs) in continuously embedded Hilbert spaces with non-smooth coefficients. Furthermore, we establish a link between invariance of submanifolds for such SPDEs in Hermite Sobolev spaces and invariance of submanifolds for finite dimensional SDEs. This provides a new method for analyzing stochastic invariance of submanifolds for finite dimensional Itô diffusions, which we will use in order to derive new invariance results for finite dimensional SDEs.

74 pages

References in corpus (1)

• Affine realizations with affine state processes for stochastic partial differential equations

Cited by in corpus (1)

• A note on invariant manifolds for stochastic partial differential equations in the framework of the variational approach