English

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