Lucas Coeuret
Published 2022-01-05, updated 2022-11-15Version 2
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.
On the central and local limit theorem for martingale difference sequences
A Local Limit Theorem for the Minimum of a Random Walk with Markovian Increasements
A local limit theorem for random walks on the chambers of $\tilde{A}_2$ buildings
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