Asymptotic expansions for potential functions of I.I.D. random fields
type: Item
instance of: scholarly article
title: Asymptotic expansions for potential functions of I.I.D. random fields
zbMATH Open document ID: 0659.60035
DOI: 10.1007/BF00339992
publication date: 1989-01-01T00:00:00Z
review text: For sums of finite range potential functions of an iid random field we derive the validity of formal expansions of length two. Under standard conditions, formal expansions are valid if and only if the characteristic functions of the sum converge to zero for all nonzero frequency parameters. If this convergence fails, the distribution of the sum can be approximated by a mixture of lattice distributions. The result applies to m-dependent random fields generated by independent random variables.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 4078367
zbMATH Keywords: central limit theorem
zbMATH Keywords: Edgeworth expansions
zbMATH Keywords: m-dependence
zbMATH Keywords: random fields
zbMATH Keywords: finite range potential functions
zbMATH Keywords: mixture of lattice distributions
author: Friedrich Götze
author: Christian Hipp
reviewed by: Friedrich Götze
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00339992
OpenAlex ID: W2095343993
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4078367