Averaging principle for slow-fast systems of rough differential equations via controlled paths
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866908336833691648 |
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| author | Inahama, Yuzuru |
| author_facet | Inahama, Yuzuru |
| contents | In this paper we prove the strong averaging principle for a slow-fast system of rough differential equations. The slow and the fast component of the system are driven by a rather general random rough path and Brownian rough path, respectively. These two driving noises are assumed to be independent. A prominent example of the driver of the slow component is fractional Brownian rough path with Hurst parameter between 1/3 and 1/2. We work in the framework of controlled path theory, which is one of the most widely-used frameworks in rough path theory. To prove our main theorem, we carry out Khas'minskii's time-discretizing method in this framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_01334 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Averaging principle for slow-fast systems of rough differential equations via controlled paths Inahama, Yuzuru Probability Dynamical Systems 60L90 (Primary) 70K65, 70K70, 60F99 (Secondary) In this paper we prove the strong averaging principle for a slow-fast system of rough differential equations. The slow and the fast component of the system are driven by a rather general random rough path and Brownian rough path, respectively. These two driving noises are assumed to be independent. A prominent example of the driver of the slow component is fractional Brownian rough path with Hurst parameter between 1/3 and 1/2. We work in the framework of controlled path theory, which is one of the most widely-used frameworks in rough path theory. To prove our main theorem, we carry out Khas'minskii's time-discretizing method in this framework. |
| title | Averaging principle for slow-fast systems of rough differential equations via controlled paths |
| topic | Probability Dynamical Systems 60L90 (Primary) 70K65, 70K70, 60F99 (Secondary) |
| url | https://arxiv.org/abs/2210.01334 |