Variations de champs Gaussiens stationnaires: Application à l'idéntification. (Variations of stationary Gaussian fields: Application to identification)
type: Item
instance of: scholarly article
title: Variations de champs Gaussiens stationnaires: Application à l'idéntification. (Variations of stationary Gaussian fields: Application to identification)
zbMATH Open document ID: 0596.60051
DOI: 10.1007/BF00354032
author: Xavier Guyon
publication date: 1987-01-01T00:00:00Z
review text: Let \((X_ t\), \(t\in {\mathbb{R}}^ d)\) be a stationary Gaussian random field, with covariance R. For \(d=1\) and \(d=2\), families of variations are described. The convergence in mean square of these variations and a subsequent identification of a model for X are studied. Under suitable global conditions for R, the behaviour of these variations depends on the local behaviour of R near the origin. The differences between the case \(d=1\) and \(d=2\) are particularly emphasised: for \(d=1\), there exists only one variation; for \(d=2\), several families of variations are available which provided a useful tool for identifying different models: for example, Ornstein-Uhlenbeck processes can be identified in mean square on \({\mathbb{R}}^ 2\), but not on \({\mathbb{R}}^ 1\).
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 3960683
zbMATH Keywords: stationary Gaussian random field
zbMATH Keywords: convergence in mean square
zbMATH Keywords: Ornstein- Uhlenbeck processes
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3960683