On the rate of convergence of the martingale central limit theorem in Wasserstein distances
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911965586128896 |
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| author | Guo, Xiaoqin |
| author_facet | Guo, Xiaoqin |
| contents | For martingales with a wide range of integrability, we will quantify the rate of convergence of the central limit theorem via Wasserstein distances of order $r$, $1\le r\le 3$. Our bounds are in terms of Lyapunov's coefficients and the $\mathscr L^{r/2}$ fluctuation of the total conditional variances. We will show that our Wasserstein-1 bound is optimal up to a multiplicative constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16980 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the rate of convergence of the martingale central limit theorem in Wasserstein distances Guo, Xiaoqin Probability 60G42, 60F05, 60B10 For martingales with a wide range of integrability, we will quantify the rate of convergence of the central limit theorem via Wasserstein distances of order $r$, $1\le r\le 3$. Our bounds are in terms of Lyapunov's coefficients and the $\mathscr L^{r/2}$ fluctuation of the total conditional variances. We will show that our Wasserstein-1 bound is optimal up to a multiplicative constant. |
| title | On the rate of convergence of the martingale central limit theorem in Wasserstein distances |
| topic | Probability 60G42, 60F05, 60B10 |
| url | https://arxiv.org/abs/2407.16980 |