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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.07538 |
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| _version_ | 1866918088225587200 |
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| author | Li, Yueling Sun, Xiaobin Wang, Zijuan Xie, Yingchao |
| author_facet | Li, Yueling Sun, Xiaobin Wang, Zijuan Xie, Yingchao |
| contents | This paper considers a class of nonautonomous slow-fast stochastic partial differential equations driven by $α$-stable processes for $α\in (1,2)$. By introducing the evolution system of measures, we establish an averaging principle for this stochastic system. Specifically, we first prove the strong convergence (in the $L^p$ sense for $p\in (1,α)$) of the slow component to the solution of a simplified averaged equation with coefficients depend on the scaling parameter. Furthermore, under conditions that coefficients are time-periodic or satisfy certain asymptotic convergence, we prove that the slow component converges strongly to the solution of an averaged equation, whose coefficients are independent of the scaling parameter. Finally, a concrete example is provided to illustrate the applicability of our assumptions. Notably, the absence of finite second moments in the solution caused by the $α$-stable processes requires new technical treatments, thereby solving a problem mentioned in [1,Remark 3.3]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong averaging principle for nonautonomous slow-fast SPDEs driven by $α$-stable processes Li, Yueling Sun, Xiaobin Wang, Zijuan Xie, Yingchao Probability 60H35 This paper considers a class of nonautonomous slow-fast stochastic partial differential equations driven by $α$-stable processes for $α\in (1,2)$. By introducing the evolution system of measures, we establish an averaging principle for this stochastic system. Specifically, we first prove the strong convergence (in the $L^p$ sense for $p\in (1,α)$) of the slow component to the solution of a simplified averaged equation with coefficients depend on the scaling parameter. Furthermore, under conditions that coefficients are time-periodic or satisfy certain asymptotic convergence, we prove that the slow component converges strongly to the solution of an averaged equation, whose coefficients are independent of the scaling parameter. Finally, a concrete example is provided to illustrate the applicability of our assumptions. Notably, the absence of finite second moments in the solution caused by the $α$-stable processes requires new technical treatments, thereby solving a problem mentioned in [1,Remark 3.3]. |
| title | Strong averaging principle for nonautonomous slow-fast SPDEs driven by $α$-stable processes |
| topic | Probability 60H35 |
| url | https://arxiv.org/abs/2507.07538 |