Local limit theorem for complex valued sequences
Probability
2025-02-25 v2 Numerical Analysis
Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2201.01514,
title = {Local limit theorem for complex valued sequences},
author = {Lucas Coeuret},
journal= {arXiv preprint arXiv:2201.01514},
year = {2025}
}