On the averaging theorems for stochastic perturbation of conservative linear systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913831079378944 |
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| author | Guo, Jing Kuksin, Sergei Liu, Zhenxin |
| author_facet | Guo, Jing Kuksin, Sergei Liu, Zhenxin |
| contents | For stochastic perturbations of linear systems with non-zero pure imaginary spectrum we discuss the averaging theorems in terms of the slow-fast action-angle variables and in the sense of Krylov-Bogoliubov. Then we show that if the diffusion matrix of the perturbation is uniformly elliptic, then in all cases the averaged dynamics does not depend on a hamiltonian part of the perturbation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the averaging theorems for stochastic perturbation of conservative linear systems Guo, Jing Kuksin, Sergei Liu, Zhenxin Dynamical Systems For stochastic perturbations of linear systems with non-zero pure imaginary spectrum we discuss the averaging theorems in terms of the slow-fast action-angle variables and in the sense of Krylov-Bogoliubov. Then we show that if the diffusion matrix of the perturbation is uniformly elliptic, then in all cases the averaged dynamics does not depend on a hamiltonian part of the perturbation. |
| title | On the averaging theorems for stochastic perturbation of conservative linear systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.04379 |