Article Dans Une Revue Asymptotic Analysis Année : 2025

Local Limit Theorem for Complex Valued Sequences

Résumé

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.

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Dates et versions

hal-03463375 , version 1 (09-12-2021)
hal-03463375 , version 2 (15-11-2022)

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Lucas Coeuret. Local Limit Theorem for Complex Valued Sequences. Asymptotic Analysis, 2025, ⟨10.1177/09217134241308379⟩. ⟨hal-03463375v2⟩
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