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The local limit theorem for complex valued sequences: the parabolic case (2408.12876v2)
Published 23 Aug 2024 in math.NA and cs.NA
Abstract: We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in probability theory for random walks as well as in numerical analysis for studying the large time behavior of numerical schemes.