An elementary proof of the local central limit theorem
type: Item
instance of: scholarly article
title: An elementary proof of the local central limit theorem
zbMATH Open document ID: 0841.60013
DOI: 10.1007/BF02218051
author: Burgess Davis
author: David R. Mcdonald
published in: Journal of Theoretical Probability
publication date: 1996-07-18T00:00:00Z
review text: The authors give a proof (characteristic functions free) of the local central limit theorem for independent non-identically distributed integer valued random variables. The first theorem is formulated for the sum of \(n\) random variables. This theorem is restated for the triangular arrays of variables. The theorems have some interesting consequences. The vector-variable analog of the second theorem is also proved for an array of independent \(L\)-valued random vectors. \(L\) denotes the \(d\)-dimensional integer lattice.
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 806436
zbMATH Keywords: central limit theorem
zbMATH Keywords: triangular arrays
reviewed by: Pavel Froněk
MaRDI profile type: Publication
cites work: On the Application of a Smoothness Function in Proving a Local Limit Theorem
cites work: On Local Limit Theorem for Integer-Valued Random Variables
cites work: Q4821326
cites work: Local Limit Theorems for Lattice Random Variables
cites work: Q5731217
full work available at URL: https://doi.org/10.1007/bf02218051
OpenAlex ID: W1973991661
description: scientific article; zbMATH DE number 806436