On Mukhin's necessary and sufficient condition for the validity of the local limit theorem
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917714110447616 |
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| author | Weber, Michel J. G. |
| author_facet | Weber, Michel J. G. |
| contents | Mukhin found in 1984 an important necessary and sufficient condition for the validity of the local limit theorem. Revisiting the succint proof given in \cite{Mu2}, we could only prove rigorously a weaker necessary and sufficient condition, with a significantly different formulation. This is the object of this short Note. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_07968 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Mukhin's necessary and sufficient condition for the validity of the local limit theorem Weber, Michel J. G. Probability Primary: 60F15, 60G50, Secondary: 60F05 Mukhin found in 1984 an important necessary and sufficient condition for the validity of the local limit theorem. Revisiting the succint proof given in \cite{Mu2}, we could only prove rigorously a weaker necessary and sufficient condition, with a significantly different formulation. This is the object of this short Note. |
| title | On Mukhin's necessary and sufficient condition for the validity of the local limit theorem |
| topic | Probability Primary: 60F15, 60G50, Secondary: 60F05 |
| url | https://arxiv.org/abs/2209.07968 |