Richter's local limit theorem,its refinement,and related results

TL;DR

This paper provides a detailed proof and refinement of Richter's local limit theorem, demonstrating the stability of the remainder term under small distribution perturbations and discussing related bounds for characteristic functions and Laplace transforms.

Contribution

It offers a refined proof of Richter's local limit theorem and establishes the stability of its remainder term under small distribution perturbations.

Findings

Refined proof of Richter's local limit theorem

Stability of the remainder term under perturbations

Quantitative bounds for characteristic functions and Laplace transforms

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.