Wasserstein convergence rates in the invariance principle for sequential dynamical systems
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914992487399424 |
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| author | Liu, Zhenxin Wang, Zhe |
| author_facet | Liu, Zhenxin Wang, Zhe |
| contents | In this paper, we consider the convergence rate with respect to the Wasserstein distance in the invariance principle for sequential dynamical systems. We utilize and modify the techniques previously employed for stationary sequences to address our non-stationary case. Under certain assumptions, we can apply our result to a large class of dynamical systems, including sequential $β_n$-transformations, piecewise uniformly expanding maps with additive noise in one-dimensional and multidimensional case, and so on. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13913 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Wasserstein convergence rates in the invariance principle for sequential dynamical systems Liu, Zhenxin Wang, Zhe Dynamical Systems 37A50, 60F17, 37C99, 60B10 In this paper, we consider the convergence rate with respect to the Wasserstein distance in the invariance principle for sequential dynamical systems. We utilize and modify the techniques previously employed for stationary sequences to address our non-stationary case. Under certain assumptions, we can apply our result to a large class of dynamical systems, including sequential $β_n$-transformations, piecewise uniformly expanding maps with additive noise in one-dimensional and multidimensional case, and so on. |
| title | Wasserstein convergence rates in the invariance principle for sequential dynamical systems |
| topic | Dynamical Systems 37A50, 60F17, 37C99, 60B10 |
| url | https://arxiv.org/abs/2307.13913 |