Strong and weak rates of convergence in the Smoluchowski--Kramers approximation for stochastic partial differential equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| author | Bréhier, Charles-Edouard Lei, Ziyi |
| author_facet | Bréhier, Charles-Edouard Lei, Ziyi |
| contents | We consider a class of stochastic damped semilinear wave equations, in the small-mass limit. It has previously been established that the solution converges to the solution of a stochastic semilinear heat equation. In this work we exhibit strong and weak rates of convergence in this Smoluchowski--Kramers approximation result. The rates depend on the regularity of the driving Wiener process. For instance, for trace-class noise the strong and weak rates of convergence are $1$, whereas for space-time white noise (in dimension $1$) the strong and weak rates of convergence are $1/2$ and $1$ respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14752 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strong and weak rates of convergence in the Smoluchowski--Kramers approximation for stochastic partial differential equations Bréhier, Charles-Edouard Lei, Ziyi Probability Analysis of PDEs We consider a class of stochastic damped semilinear wave equations, in the small-mass limit. It has previously been established that the solution converges to the solution of a stochastic semilinear heat equation. In this work we exhibit strong and weak rates of convergence in this Smoluchowski--Kramers approximation result. The rates depend on the regularity of the driving Wiener process. For instance, for trace-class noise the strong and weak rates of convergence are $1$, whereas for space-time white noise (in dimension $1$) the strong and weak rates of convergence are $1/2$ and $1$ respectively. |
| title | Strong and weak rates of convergence in the Smoluchowski--Kramers approximation for stochastic partial differential equations |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2604.14752 |