Richter's local limit theorem,its refinement,and related results
Classical Analysis and ODEs
2023-08-04 v2 Probability
Abstract
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.
Keywords
Cite
@article{arxiv.2208.09534,
title = {Richter's local limit theorem,its refinement,and related results},
author = {Sergey Bobkov and Gennadiy Chistyakov and Friedrich Götze},
journal= {arXiv preprint arXiv:2208.09534},
year = {2023}
}
Comments
Revised version with improved error bounds and dedication to the memory of Gennadiy P. Chistyakov