Variations de champs Gaussiens stationnaires: Application à l'idéntification. (Variations of stationary Gaussian fields: Application to identification)
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 \({\mathbb{R}}^ 1\).
scientific article; zbMATH DE number 3960683