Variations de champs gaussiens stationnaires: application a l'identification |
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Authors: | Xavier Guyon |
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Affiliation: | (1) Université de Paris I, 12 Place du Panthéon, F-75005 Paris, France |
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Abstract: | Summary Let 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 glocal 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, Orstein-Uhlenbeck processes can be identified in mean square on , but not on .
Variations de champs gaussiens stationnaires: application a l'identification |
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