Weak error analysis for a nonlinear SPDE approximation of the Dean-Kawasaki equation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929391352676352 |
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| author | Djurdjevac, Ana Kremp, Helena Perkowski, Nicolas |
| author_facet | Djurdjevac, Ana Kremp, Helena Perkowski, Nicolas |
| contents | We consider a nonlinear SPDE approximation of the Dean-Kawasaki equation for independent particles. Our approximation satisfies the physical constraints of the particle system, i.e. its solution is a probability measure for all times (preservation of positivity and mass conservation). Using a duality argument, we prove that the weak error between particle system and nonlinear SPDE is of the order $N^{-1-1/(d/2+1)}\log (N)$. Along the way we show well-posedness, a comparison principle and an entropy estimate for a class of nonlinear regularized Dean-Kawasaki equations with Itô noise. Keywords: Dean-Kawasaki equation, weak error analysis, Laplace duality |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11714 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Weak error analysis for a nonlinear SPDE approximation of the Dean-Kawasaki equation Djurdjevac, Ana Kremp, Helena Perkowski, Nicolas Probability 60H17, 60H35 We consider a nonlinear SPDE approximation of the Dean-Kawasaki equation for independent particles. Our approximation satisfies the physical constraints of the particle system, i.e. its solution is a probability measure for all times (preservation of positivity and mass conservation). Using a duality argument, we prove that the weak error between particle system and nonlinear SPDE is of the order $N^{-1-1/(d/2+1)}\log (N)$. Along the way we show well-posedness, a comparison principle and an entropy estimate for a class of nonlinear regularized Dean-Kawasaki equations with Itô noise. Keywords: Dean-Kawasaki equation, weak error analysis, Laplace duality |
| title | Weak error analysis for a nonlinear SPDE approximation of the Dean-Kawasaki equation |
| topic | Probability 60H17, 60H35 |
| url | https://arxiv.org/abs/2212.11714 |