Local limit theorem in the case of convergence to a law of class L
type: Item
instance of: scholarly article
title: Local limit theorem in the case of convergence to a law of class L
zbMATH Open document ID: 0651.60026
DOI: 10.1007/BF00971916
author: A. Mitalauskas
published in: Lithuanian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Suppose \(\{\xi_ 1,\xi_ 2,...\}\) is a sequence of integer-valued independent random variables. Let \(S_ n\) denote its partial sum of first n elements. Assume \(\{B_ n\}\), \(\{a_ n\}\) are two sequences of constants such that \(S_ n/B_ n-a_ n\) tends in distribution to an L- class distribution with density p. Then the local limit theorem for the sequence \(\{\xi_ n\}\) is defined as \[ \sup_{m}| B_ nP(S_ n=m)-p(m/B_ n-a_ n)| \to 0,\quad as\quad n\to \infty. \] Certain sufficient conditions are given for guaranteeing the local limit theorem.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 4062249
zbMATH Keywords: L-class distribution
zbMATH Keywords: infinitely divisible distribution
zbMATH Keywords: local limit theorem
Wikidata QID: Q114852761
MaRDI profile type: Publication
cites work: On distribution functions of class L
cites work: Q5737409
full work available at URL: https://doi.org/10.1007/bf00971916
OpenAlex ID: W1991570688
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description: scientific article; zbMATH DE number 4062249