Averaging principle for semilinear slow-fast rough partial differential equations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916492946178048 |
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| author | Li, Miaomiao Li, Yunzhang Pei, Bin Xu, Yong |
| author_facet | Li, Miaomiao Li, Yunzhang Pei, Bin Xu, Yong |
| contents | In this paper, we investigate the averaging principle for a class of semilinear slow-fast partial differential equations driven by finite-dimensional rough multiplicative noise. Specifically, the slow component is driven by a general random $γ$-Hölder rough path for some $γ\in (1/3,1/2)$, while the fast component is driven by a Brownian rough path. Using controlled rough path theory and the classical Khasminskii's time discretization scheme, we demonstrate that the slow component converges strongly to the solution of the corresponding averaged equation under the Hölder topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Averaging principle for semilinear slow-fast rough partial differential equations Li, Miaomiao Li, Yunzhang Pei, Bin Xu, Yong Probability In this paper, we investigate the averaging principle for a class of semilinear slow-fast partial differential equations driven by finite-dimensional rough multiplicative noise. Specifically, the slow component is driven by a general random $γ$-Hölder rough path for some $γ\in (1/3,1/2)$, while the fast component is driven by a Brownian rough path. Using controlled rough path theory and the classical Khasminskii's time discretization scheme, we demonstrate that the slow component converges strongly to the solution of the corresponding averaged equation under the Hölder topology. |
| title | Averaging principle for semilinear slow-fast rough partial differential equations |
| topic | Probability |
| url | https://arxiv.org/abs/2411.06089 |