Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908491227070464 |
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| author | Chandra, Ajay Chevyrev, Ilya |
| author_facet | Chandra, Ajay Chevyrev, Ilya |
| contents | We propose an elementary method to show non-Gaussianity of invariant measures of parabolic stochastic partial differential equations with polynomial non-linearities in the Da Prato--Debussche regime. The approach is essentially algebraic and involves using the generator equation of the SPDE at stationarity. Our results in particular cover the $Φ^4_δ$ measures in dimensions $δ<\frac{14}{5}$, which includes cases where the invariant measure is singular with respect to the invariant measure of the linear solution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_06612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime Chandra, Ajay Chevyrev, Ilya Probability We propose an elementary method to show non-Gaussianity of invariant measures of parabolic stochastic partial differential equations with polynomial non-linearities in the Da Prato--Debussche regime. The approach is essentially algebraic and involves using the generator equation of the SPDE at stationarity. Our results in particular cover the $Φ^4_δ$ measures in dimensions $δ<\frac{14}{5}$, which includes cases where the invariant measure is singular with respect to the invariant measure of the linear solution. |
| title | Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime |
| topic | Probability |
| url | https://arxiv.org/abs/2501.06612 |