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
On the local limit theorems for lower psi-mixing Markov chains
Asymptotic Expansions for the Sojourn Time Distribution in the $M/G/1$-PS Queue
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