A quantitative CLT on a finite sum of Wiener chaoses and applications to ratios of Gaussian functionals
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908407553851392 |
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| author | Es-Sebaiy, Khalifa |
| author_facet | Es-Sebaiy, Khalifa |
| contents | In this paper we provide a new explicit bound on the total variation distance between a standardized partial sum of random variables belonging to a finite sum of Wiener chaoses and a standard normal random variable. We apply our result to derive an upper bound for the Kolmogorov distance between a ratio of multiple stochastic integrals and a Gaussian random variable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16991 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A quantitative CLT on a finite sum of Wiener chaoses and applications to ratios of Gaussian functionals Es-Sebaiy, Khalifa Probability 60G15, 60F05, 60H07 In this paper we provide a new explicit bound on the total variation distance between a standardized partial sum of random variables belonging to a finite sum of Wiener chaoses and a standard normal random variable. We apply our result to derive an upper bound for the Kolmogorov distance between a ratio of multiple stochastic integrals and a Gaussian random variable. |
| title | A quantitative CLT on a finite sum of Wiener chaoses and applications to ratios of Gaussian functionals |
| topic | Probability 60G15, 60F05, 60H07 |
| url | https://arxiv.org/abs/2412.16991 |