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

2021/11/23 by B. Rajeev, Bhaskaran, Rajeev, Stefan Tappe +1
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2111.11735

openalex publication_date 2021/11/23 · openalex created_date 2021/12/06 · openalex updated_date 2026/07/28

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.

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