We give a detailed exposition of the proof of Richter’s local limit theorem in a refined form and establish the stability of the remainder term in this theorem under small perturbations of the underlying distribution (including smoothing).We also discuss related quantitative bounds for characteristic functions and Laplace transforms.
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In memoriam Gennadiy P. Chistyakov (May 1, 1945 – December 30, 2022)
*Research supported by the NSF grant DMS-2154001 and the GRF – SFB 1283/2 2021 – 317210226.
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Bobkov, S.G., Chistyakov, G.P. & Götze, F. Richter’s local limit theorem, its refinement, and related results*. Lith Math J 63, 138–160 (2023). https://doi.org/10.1007/s10986-023-09598-9
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DOI: https://doi.org/10.1007/s10986-023-09598-9