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Local limit theorem for complex valued sequences (2201.01514v2)
Published 5 Jan 2022 in math.PR, cs.NA, and math.NA
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.