Invariant manifolds for stochastic partial differential equations in continuously embedded Hilbert spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866917094136741888 |
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| author | Bhaskaran, Rajeev Tappe, Stefan |
| author_facet | Bhaskaran, Rajeev Tappe, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_11735 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Invariant manifolds for stochastic partial differential equations in continuously embedded Hilbert spaces Bhaskaran, Rajeev Tappe, Stefan Probability Functional Analysis 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. |
| title | Invariant manifolds for stochastic partial differential equations in continuously embedded Hilbert spaces |
| topic | Probability Functional Analysis |
| url | https://arxiv.org/abs/2111.11735 |