The local limit problem and Hölder-continuity
type: Item
instance of: scholarly article
title: The local limit problem and Hölder-continuity
zbMATH Open document ID: 0659.60037
DOI: 10.1007/BF00354765
author: Wolfgang Macht
author: Werner Wolf
publication date: 1989-01-01T00:00:00Z
review text: The local limit problem is investigated for sequences \((p_ n)\) of probability densities with stable limit densities \(q_{\alpha}\) having characteristic exponent \(\alpha\in (0,2]\). It is shown that certain continuity-properties (Hölder-continuity) are necessary and - under appropriate additionl conditions - sufficient for \[ \sup_{x}| p_ n(x)-q_{\alpha}(x)| \to 0\quad as\quad n\to \infty. \] In this sense the speed of convergence is also studied.
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 4078369
zbMATH Keywords: local limit problem
zbMATH Keywords: stable limit densities
zbMATH Keywords: continuity-properties
zbMATH Keywords: speed of convergence
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4078369