The Smoluchowski-Kramers approximation for a system with arbitrary friction depending on both state and distribution
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929400473190400 |
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| author | Liu, Xueru Jiang, Qianqian Wang, Wei |
| author_facet | Liu, Xueru Jiang, Qianqian Wang, Wei |
| contents | A system of stochastic differential equations describing diffusive phenomena, which has arbitrary friction depending on both state and distribution is investigated. The Smoluchowski-Kramers approximation is seen to describe dynamics in the small mass limit. We obtain the limiting equation and, in particular, the addition drift terms that appear in the limiting equation are expressed in terms of the solutions to the Lyapunov matrix equation and Sylvester matrix equation. Furthermore, we provide the rate of convergence and extend the system to encompass more general interactions and noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18056 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Smoluchowski-Kramers approximation for a system with arbitrary friction depending on both state and distribution Liu, Xueru Jiang, Qianqian Wang, Wei Probability 60 A system of stochastic differential equations describing diffusive phenomena, which has arbitrary friction depending on both state and distribution is investigated. The Smoluchowski-Kramers approximation is seen to describe dynamics in the small mass limit. We obtain the limiting equation and, in particular, the addition drift terms that appear in the limiting equation are expressed in terms of the solutions to the Lyapunov matrix equation and Sylvester matrix equation. Furthermore, we provide the rate of convergence and extend the system to encompass more general interactions and noise. |
| title | The Smoluchowski-Kramers approximation for a system with arbitrary friction depending on both state and distribution |
| topic | Probability 60 |
| url | https://arxiv.org/abs/2406.18056 |