Rates of convergence in CLT and ASIP for sequences of expanding maps
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910299438710784 |
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| author | Dolgopyat, Dmitry Hafouta, Yeor |
| author_facet | Dolgopyat, Dmitry Hafouta, Yeor |
| contents | We prove Berry-Esseen theorems and the almost sure invariance principle with rates for partial sums of the form $S_n=\sum_{j=0}^{n-1}f_j\circ T_{j-1}\circ\cdots\circ T_1\circ T_0$ where $f_j$ are functions with uniformly bounded ``variation" and $T_j$ is a sequence of expanding maps. Using symbolic representations similar result follow for maps $T_j$ in a small $C^1$ neighborhood of an Axiom A map and Hölder continuous functions $f_j$. All of our results are already new for a single map $T_j=T$ and a sequence of different functions $(f_j)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08802 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rates of convergence in CLT and ASIP for sequences of expanding maps Dolgopyat, Dmitry Hafouta, Yeor Dynamical Systems Probability We prove Berry-Esseen theorems and the almost sure invariance principle with rates for partial sums of the form $S_n=\sum_{j=0}^{n-1}f_j\circ T_{j-1}\circ\cdots\circ T_1\circ T_0$ where $f_j$ are functions with uniformly bounded ``variation" and $T_j$ is a sequence of expanding maps. Using symbolic representations similar result follow for maps $T_j$ in a small $C^1$ neighborhood of an Axiom A map and Hölder continuous functions $f_j$. All of our results are already new for a single map $T_j=T$ and a sequence of different functions $(f_j)$. |
| title | Rates of convergence in CLT and ASIP for sequences of expanding maps |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2401.08802 |