Richter’s local limit theorem, its refinement, and related results*

Sergey G. Bobkov; Gennadiy P. Chistyakov; Friedrich Götze

doi:10.1007/s10986-023-09598-9

Richter’s local limit theorem, its refinement, and related results*

Sergey G. Bobkov
, Gennadiy P. Chistyakov
, Friedrich Götze

School of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English (US)
Pages (from-to)	138-160
Number of pages	23
Journal	Lithuanian Mathematical Journal
Volume	63
Issue number	2
DOIs	https://doi.org/10.1007/s10986-023-09598-9
State	Published - Apr 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s).

Keywords

central limit theorem
characteristic functions
local limit theorem

Publisher link

10.1007/s10986-023-09598-9

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abstract = "We give a detailed exposition of the proof of Richter{\textquoteright}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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T1 - Richter’s local limit theorem, its refinement, and related results*

AU - Bobkov, Sergey G.

AU - Chistyakov, Gennadiy P.

AU - Götze, Friedrich

PY - 2023/4

Y1 - 2023/4

N2 - 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.

AB - 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.

KW - central limit theorem

KW - characteristic functions

KW - local limit theorem

UR - https://www.scopus.com/pages/publications/85165628532

UR - https://www.scopus.com/pages/publications/85165628532#tab=citedBy

U2 - 10.1007/s10986-023-09598-9

DO - 10.1007/s10986-023-09598-9

M3 - Article

AN - SCOPUS:85165628532

SN - 0363-1672

VL - 63

SP - 138

EP - 160

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

IS - 2

ER -

Richter’s local limit theorem, its refinement, and related results*

Abstract

Bibliographical note

Keywords

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