Characterizing models in regularity structures: a quasilinear case
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915332007919616 |
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| author | Tempelmayr, Markus |
| author_facet | Tempelmayr, Markus |
| contents | We give a novel characterization of the centered model in regularity structures which persists for rough drivers even as a mollification fades away. We present our result for a class of quasilinear equations driven by noise, however we believe that the method is robust and applies to a much broader class of subcritical equations. Furthermore, we prove that a convergent sequence of noise ensembles, satisfying uniformly a spectral gap assumption, implies the corresponding convergence of the associated models. Combined with the characterization, this establishes a universality-type result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_18192 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterizing models in regularity structures: a quasilinear case Tempelmayr, Markus Probability Analysis of PDEs 60H17, 60L30, 60H07 We give a novel characterization of the centered model in regularity structures which persists for rough drivers even as a mollification fades away. We present our result for a class of quasilinear equations driven by noise, however we believe that the method is robust and applies to a much broader class of subcritical equations. Furthermore, we prove that a convergent sequence of noise ensembles, satisfying uniformly a spectral gap assumption, implies the corresponding convergence of the associated models. Combined with the characterization, this establishes a universality-type result. |
| title | Characterizing models in regularity structures: a quasilinear case |
| topic | Probability Analysis of PDEs 60H17, 60L30, 60H07 |
| url | https://arxiv.org/abs/2303.18192 |