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arXiv · 2111.11735

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

Rajeev Bhaskaran·Stefan Tappe
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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 It\^{o} diffusions, which we will use in order to derive new invariance results for finite dimensional SDEs.

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Rajeev Bhaskaran, Stefan Tappe. 2021-11-23. Invariant manifolds for stochastic partial differential equations in continuously embedded Hilbert spaces. https://doi.org/10.1007/s11118-024-10134-8

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