Energy solutions of singular SPDEs on Hilbert spaces with applications to domains with boundary conditions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914492644851712 |
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| author | Gräfner, Lukas Perkowski, Nicolas Popat, Shyam |
| author_facet | Gräfner, Lukas Perkowski, Nicolas Popat, Shyam |
| contents | In this paper we extend the theory of energy solutions for singular SPDEs, focusing on equations driven by highly irregular noise with bilinear nonlinearities, including scaling critical examples. By introducing Gelfand triples and leveraging infinite-dimensional analysis in Hilbert spaces together with an integration by parts formula under the invariant measure, we largely eliminate the need for Fourier series and chaos expansions. This approach broadens the applicability of energy solutions to a wider class of SPDEs, offering a unified treatment of various domains and boundary conditions. Our examples are motivated by recent work on scaling limits of interacting particle systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07680 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Energy solutions of singular SPDEs on Hilbert spaces with applications to domains with boundary conditions Gräfner, Lukas Perkowski, Nicolas Popat, Shyam Probability Analysis of PDEs 60H17, 60H07, 60H50 In this paper we extend the theory of energy solutions for singular SPDEs, focusing on equations driven by highly irregular noise with bilinear nonlinearities, including scaling critical examples. By introducing Gelfand triples and leveraging infinite-dimensional analysis in Hilbert spaces together with an integration by parts formula under the invariant measure, we largely eliminate the need for Fourier series and chaos expansions. This approach broadens the applicability of energy solutions to a wider class of SPDEs, offering a unified treatment of various domains and boundary conditions. Our examples are motivated by recent work on scaling limits of interacting particle systems. |
| title | Energy solutions of singular SPDEs on Hilbert spaces with applications to domains with boundary conditions |
| topic | Probability Analysis of PDEs 60H17, 60H07, 60H50 |
| url | https://arxiv.org/abs/2411.07680 |