Local limit theorem for complex valued sequences
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912240336109568 |
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| author | Coeuret, Lucas |
| author_facet | Coeuret, Lucas |
| contents | In this article, we study the pointwise asymptotic behavior of iterated convolutions on the one dimensional lattice Z. We generalize the so-called local limit theorem in probability theory to complex valued sequences. A sharp rate of convergence towards an explicitly computable attractor is proved together with a generalized Gaussian bound for the asymptotic expansion up to any order of the iterated convolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_01514 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Local limit theorem for complex valued sequences Coeuret, Lucas Probability Numerical Analysis 42A85, 35K25, 60F99, 65M12 In this article, we study the pointwise asymptotic behavior of iterated convolutions on the one dimensional lattice Z. We generalize the so-called local limit theorem in probability theory to complex valued sequences. A sharp rate of convergence towards an explicitly computable attractor is proved together with a generalized Gaussian bound for the asymptotic expansion up to any order of the iterated convolution. |
| title | Local limit theorem for complex valued sequences |
| topic | Probability Numerical Analysis 42A85, 35K25, 60F99, 65M12 |
| url | https://arxiv.org/abs/2201.01514 |