Richter's local limit theorem,its refinement,and related results
Sergey Bobkov, Gennadiy Chistyakov, Friedrich G\"otze

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.
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Taxonomy
TopicsFunctional Equations Stability Results · Mathematical functions and polynomials · Advanced Banach Space Theory
