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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.06653 |
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| _version_ | 1866917105818927104 |
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| author | Jonas, Lena Mattner, Lutz |
| author_facet | Jonas, Lena Mattner, Lutz |
| contents | We prove a central limit error bound for convolution powers of laws with finite moments of order $r \in \mathopen]2,3\mathclose]$, taking a closeness of the laws to normality into account. Up to a universal constant, this generalises the case of $r=3$ of the sharpening of the Berry (1941) - Esseen (1942) theorem obtained by Mattner (2024), namely by sharpening here the Katz (1963) error bound for the i.i.d. case of Lyapunov's (1901) theorem. Our proof uses a partial generalisation of the theorem of Senatov and Zolotarev (1986) used for the earlier special case. A result more general than our main one could be obtained by using instead another theorem of Senatov (1980), but unfortunately an auxiliary inequality used in the latter's proof is wrong. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06653 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A sharper Lyapunov-Katz central limit error bound for i.i.d. summands Zolotarev-close to normal Jonas, Lena Mattner, Lutz Probability Primary 60F05, 60E15 We prove a central limit error bound for convolution powers of laws with finite moments of order $r \in \mathopen]2,3\mathclose]$, taking a closeness of the laws to normality into account. Up to a universal constant, this generalises the case of $r=3$ of the sharpening of the Berry (1941) - Esseen (1942) theorem obtained by Mattner (2024), namely by sharpening here the Katz (1963) error bound for the i.i.d. case of Lyapunov's (1901) theorem. Our proof uses a partial generalisation of the theorem of Senatov and Zolotarev (1986) used for the earlier special case. A result more general than our main one could be obtained by using instead another theorem of Senatov (1980), but unfortunately an auxiliary inequality used in the latter's proof is wrong. |
| title | A sharper Lyapunov-Katz central limit error bound for i.i.d. summands Zolotarev-close to normal |
| topic | Probability Primary 60F05, 60E15 |
| url | https://arxiv.org/abs/2503.06653 |