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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2403.16349 |
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| _version_ | 1866908888385716224 |
|---|---|
| author | Leppänen, Juho |
| author_facet | Leppänen, Juho |
| contents | We adapt Stein's method to obtain Berry--Esseen type error bounds in the multivariate central limit theorem for non-stationary processes generated by time-dependent compositions of uniformly expanding dynamical systems. In a particular case of random dynamical systems with a strongly mixing base transformation, we derive an error estimate of order $O(N^{-1/2})$ in the quenched multivariate CLT, provided that the covariance matrix "grows linearly" with the number of summands $N$. The error in the normal approximation is estimated for the class of all convex sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16349 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A multivariate Berry--Esseen theorem for time-dependent expanding dynamical systems Leppänen, Juho Dynamical Systems Probability We adapt Stein's method to obtain Berry--Esseen type error bounds in the multivariate central limit theorem for non-stationary processes generated by time-dependent compositions of uniformly expanding dynamical systems. In a particular case of random dynamical systems with a strongly mixing base transformation, we derive an error estimate of order $O(N^{-1/2})$ in the quenched multivariate CLT, provided that the covariance matrix "grows linearly" with the number of summands $N$. The error in the normal approximation is estimated for the class of all convex sets. |
| title | A multivariate Berry--Esseen theorem for time-dependent expanding dynamical systems |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2403.16349 |