Compound Poisson approximation for unbounded functions on a group, with application to large deviations
type: Item
instance of: scholarly article
title: Compound Poisson approximation for unbounded functions on a group, with application to large deviations
zbMATH Open document ID: 0847.60005
DOI: 10.1007/BF01246337
author: Louis H. Y. Chen
author: Małgorzata Roos
publication date: 1996-09-24T00:00:00Z
review text: The paper establishes a second order bound on the approximation of \(\int hd \widehat Q\) by \(\int hdQ\), where \(\widehat Q = \prod^n_{i = 1} [(1 - p_i)I + p_i \mu_i]\) is the convolution of \(n\) probability measures on a measurable Abelian group \((X,B)\) which are not too far from the measure \(I\) which assigns probability 1 to the identity in \(X\), and \(Q\) is a related compound Poisson measure. The bounds are in the spirit of those in [the first author and \textit{K. P. Choi}, Ann. Probab. 20, No. 4, 1867-1876 (1992; Zbl 0764.60026)], and involve making minimal assumptions on the function \(h\), yet the bounds obtained are sharp enough to yield good large deviation estimates. Multivariate Poisson approximation is discussed as a particular application.
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 60B10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 822730
zbMATH Keywords: convolution of \(n\) probability measures
zbMATH Keywords: multivariate Poisson approximation
zbMATH Keywords: large deviation estimates
reviewed by: A. D. Barbour
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01246337
OpenAlex ID: W1987068199
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 822730